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Journal articles on the topic 'Spaces of action'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Stacheli, Lynn A. "Publicity, Privacy, and Women's Political Action." Environment and Planning D: Society and Space 14, no. 5 (October 1996): 601–19. http://dx.doi.org/10.1068/d140601.

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Interpretations of women's activism depend on the ways in which analysts conceptualize the relations between privacy, publicity, and politics, in this paper the relationship between women's standing in the public sphere and their activism is problematized. Women's activism is shaped by strategic, and sometimes opportunistic, choices to locate their activism either in public or in private spaces. These choices point to the importance of reconceptualizing publicity and privacy in ways that separate the content of actions from the spaces in which action is taken. Such a distinction creates the possibility of taking private actions into public spaces and of taking public actions in private spaces. When the content of action is separated from the spaces of action, women's activism is evaluated in terms of the efficacy of various actions in either public or private spaces, rather than in terms of women's presumed lack of access to the public sphere.

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2

Abbott, Carolyn, David Hume, and Denis Osin. "Extending group actions on metric spaces." Journal of Topology and Analysis 12, no. 03 (October 1, 2018): 625–65. http://dx.doi.org/10.1142/s1793525319500584.

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We address the following natural extension problem for group actions: Given a group [Formula: see text], a subgroup [Formula: see text], and an action of [Formula: see text] on a metric space, when is it possible to extend it to an action of the whole group [Formula: see text] on a (possibly different) metric space? When does such an extension preserve interesting properties of the original action of [Formula: see text]? We begin by formalizing this problem and present a construction of an induced action which behaves well when [Formula: see text] is hyperbolically embedded in [Formula: see text]. Moreover, we show that induced actions can be used to characterize hyperbolically embedded subgroups. We also obtain some results for elementary amenable groups.

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3

Rath, N. "Cauchy action on filter spaces." Applied General Topology 20, no. 1 (April 1, 2019): 177. http://dx.doi.org/10.4995/agt.2019.10490.

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<p>A Cauchy group (G,D,·) has a Cauchy-action on a filter space (X,C), if it acts in a compatible manner. A new filter-based method is proposed in this paper for the notion of group-action, from which the properties of this action such as transitiveness and its compatibility with various modifications of the G-space (X,C) are determined. There is a close link between the Cauchy action and the induced continuous action on the underlying G-space, which is explored here. In addition, a possible extension of a Cauchy-action to the completion of the underlying G-space is discussed. These new results confirm and generalize some of the properties of group action in a topological context.</p>

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4

Caldwell, Melissa L. "Sacred Spaces and Civic Action." Religion and Society 10, no. 1 (September 1, 2019): 111–29. http://dx.doi.org/10.3167/arrs.2019.100109.

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This article examines several key sites where Russia’s civic and religious bodies intersect in pursuit of social justice goals. Based on ethnographic fieldwork among religious communities and social justice organizations in Moscow, the article focuses on the physical, social, and legal spaces where church and state, secular and sacred, civic and personal intersect and the consequences of these intersections for how Russians understand new configurations of church and state, private and public, religious and political. Of particular concern is the emergence of new forms of religious and political pluralism that transcend any one particular space, such as for worship, community life, or political support or protest, and instead reveal shifting practices and ethics of social justice that are more pluralist, progressive, and tolerant than they may appear to be to outside observers.

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5

Lee, Jongmin, Wonseok Jeon, Geon-Hyeong Kim, and Kee-Eung Kim. "Monte-Carlo Tree Search in Continuous Action Spaces with Value Gradients." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4561–68. http://dx.doi.org/10.1609/aaai.v34i04.5885.

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Monte-Carlo Tree Search (MCTS) is the state-of-the-art online planning algorithm for large problems with discrete action spaces. However, many real-world problems involve continuous action spaces, where MCTS is not as effective as in discrete action spaces. This is mainly due to common practices such as coarse discretization of the entire action space and failure to exploit local smoothness. In this paper, we introduce Value-Gradient UCT (VG-UCT), which combines traditional MCTS with gradient-based optimization of action particles. VG-UCT simultaneously performs a global search via UCT with respect to the finitely sampled set of actions and performs a local improvement via action value gradients. In the experiments, we demonstrate that our approach outperforms existing MCTS methods and other strong baseline algorithms for continuous action spaces.

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6

LEE, KYUNG BAI, and FRANK RAYMOND. "MAXIMAL TORUS ACTIONS ON SOLVMANIFOLDS AND DOUBLE COSET SPACES." International Journal of Mathematics 02, no. 01 (February 1991): 67–76. http://dx.doi.org/10.1142/s0129167x91000065.

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Any compact, connected Lie group which acts effectively on a closed aspherical manifold is a torus Tk with k ≤ rank of [Formula: see text], the center of π1 (M). When [Formula: see text], the torus action is called a maximal torus action. The authors have previously shown that many closed aspherical manifolds admit maximal torus actions. In this paper, a smooth maximal torus action is constructed on each solvmanifold. They also construct smooth maximal torus actions on some double coset spaces of general Lie groups as applications.

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7

SOŁTAN, PIOTR MIKOŁAJ. "ON QUANTUM SEMIGROUP ACTIONS ON FINITE QUANTUM SPACES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 12, no. 03 (September 2009): 503–9. http://dx.doi.org/10.1142/s0219025709003768.

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We show that a continuous action of a quantum semigroup [Formula: see text] on a finite quantum space (finite dimensional C*-algebra) preserving a faithful state comes from a continuous action of the quantum Bohr compactification [Formula: see text] of [Formula: see text]. Using the classification of continuous compact quantum group actions on M2, we give a complete description of all continuous quantum semigroup actions on this quantum space preserving a faithful state.

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8

Hu, Liangzhong, Liangyou Hu, and Adonai S. Sant'Anna. "Born–Infeld Action on Discrete Spaces." International Journal of Theoretical Physics 43, no. 2 (February 2004): 315–21. http://dx.doi.org/10.1023/b:ijtp.0000028865.39798.12.

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9

Huck, Steffen, and Jörg Oechssler. "Informational cascades with continuous action spaces." Economics Letters 60, no. 2 (August 1998): 163–66. http://dx.doi.org/10.1016/s0165-1765(98)00094-9.

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10

Gerber, Thomas. "Triple crystal action in Fock spaces." Advances in Mathematics 329 (April 2018): 916–54. http://dx.doi.org/10.1016/j.aim.2018.02.030.

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11

Di Concilio, A. "Group action on zero-dimensional spaces." Topology and its Applications 154, no. 10 (May 2007): 2050–55. http://dx.doi.org/10.1016/j.topol.2007.01.003.

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12

Mertens, Jean-François, Abraham Neyman, and Dinah Rosenberg. "Absorbing Games with Compact Action Spaces." Mathematics of Operations Research 34, no. 2 (May 2009): 257–62. http://dx.doi.org/10.1287/moor.1080.0372.

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13

Kim, Beomjoon, Kyungjae Lee, Sungbin Lim, Leslie Kaelbling, and Tomas Lozano-Perez. "Monte Carlo Tree Search in Continuous Spaces Using Voronoi Optimistic Optimization with Regret Bounds." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 06 (April 3, 2020): 9916–24. http://dx.doi.org/10.1609/aaai.v34i06.6546.

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Many important applications, including robotics, data-center management, and process control, require planning action sequences in domains with continuous state and action spaces and discontinuous objective functions. Monte Carlo tree search (MCTS) is an effective strategy for planning in discrete action spaces. We provide a novel MCTS algorithm (voot) for deterministic environments with continuous action spaces, which, in turn, is based on a novel black-box function-optimization algorithm (voo) to efficiently sample actions. The voo algorithm uses Voronoi partitioning to guide sampling, and is particularly efficient in high-dimensional spaces. The voot algorithm has an instance of voo at each node in the tree. We provide regret bounds for both algorithms and demonstrate their empirical effectiveness in several high-dimensional problems including two difficult robotics planning problems.

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14

DASKALOPOULOS, GEORGIOS, CHIKAKO MESE, ANDREW SANDERS, and ALINA VDOVINA. "Surface groups acting on spaces." Ergodic Theory and Dynamical Systems 39, no. 7 (December 4, 2017): 1843–56. http://dx.doi.org/10.1017/etds.2017.103.

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Harmonic map theory is used to show that a convex cocompact surface group action on a $\text{CAT}(-1)$ metric space fixes a convex copy of the hyperbolic plane (i.e. the action is Fuchsian) if and only if the Hausdorff dimension of the limit set of the action is equal to 1. This provides another proof of a result of Bonk and Kleiner. More generally, we show that the limit set of every convex cocompact surface group action on a $\text{CAT}(-1)$ space has Hausdorff dimension $\geq 1$, where the inequality is strict unless the action is Fuchsian.

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15

McLean, Jessica Emma, and Sara Fuller. "Action with(out) activism: understanding digital climate change action." International Journal of Sociology and Social Policy 36, no. 9/10 (September 12, 2016): 578–95. http://dx.doi.org/10.1108/ijssp-12-2015-0136.

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Purpose A recent mainstream intervention in Australia involved the creation of a climate change communication institution, the Climate Council, from crowdfunding and support in social media. Such digital action invites further examination of supporters’ motivations. The purpose of this paper is to analyse the reported intentions and interests of the Climate Council’s supporters to gain a better understanding of mainstream climate change action in digital spaces. Design/methodology/approach This paper reports on a survey that was undertaken by the Climate Council with their Founding Friends that sought to understand their motivations for supporting the institution. The survey received over 10,000 responses. From four selected questions, the paper considers all of the quantitative responses while a random sample of 100 responses was taken from the qualitative data. Findings The data show that most Climate Council supporters were motivated to maintain an institution that communicates the impacts of climate change while a minority desired more political engagement by the institution. The results capture an example of action with limited conscious activism. Originality/value Digital spaces fundamentally need the interconnections between people in order to function, in a similar way to physical spaces. Nonetheless, the power of online action, in all its contradictory forms, should not be overlooked in considering the range of possibilities available to those interested in effecting meaningful social change. Even mainstream interventions, as presented in this paper, that seem to disavow climate change activism on the whole, can nevertheless produce institutional changes that defy national governance shifts.

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16

Heneberry, Pamela, and Arthur Turner. "Critical action learning – rituals and reflective spaces." Action Learning: Research and Practice 13, no. 1 (January 2, 2016): 60–68. http://dx.doi.org/10.1080/14767333.2015.1130349.

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17

Boudreau, James W. "All-pay auctions with discrete action spaces." Applied Economics Letters 18, no. 2 (January 26, 2011): 161–62. http://dx.doi.org/10.1080/13504850903442954.

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18

OH, HEE. "LATTICE ACTION ON FINITE VOLUME HOMOGENEOUS SPACES." Journal of the Korean Mathematical Society 42, no. 4 (July 1, 2005): 635–53. http://dx.doi.org/10.4134/jkms.2005.42.4.635.

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19

Chamseddine, Ali H., and Alain Connes. "Noncommutative geometric spaces with boundary: Spectral action." Journal of Geometry and Physics 61, no. 1 (January 2011): 317–32. http://dx.doi.org/10.1016/j.geomphys.2010.10.002.

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20

Brasco, Lorenzo. "Curves of minimal action over metric spaces." Annali di Matematica Pura ed Applicata 189, no. 1 (May 5, 2009): 95–125. http://dx.doi.org/10.1007/s10231-009-0102-0.

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21

Ranjbar-Motlagh, Alireza. "The action of groups on hyperbolic spaces." Differential Geometry and its Applications 6, no. 2 (July 1996): 169–80. http://dx.doi.org/10.1016/0926-2245(96)89147-9.

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22

Pandelis, Dimitrios G. "Markov decision processes with multidimensional action spaces." European Journal of Operational Research 200, no. 2 (January 2010): 625–28. http://dx.doi.org/10.1016/j.ejor.2009.01.039.

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23

Lowe, Alan, and Bill Doolin. "Casemix accounting systems: new spaces for action." Management Accounting Research 10, no. 3 (September 1999): 181–201. http://dx.doi.org/10.1006/mare.1999.0107.

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24

Fine, Benjamin L., and Georgia Triantafillou. "On the Equivariant Formality of Kähler Manifolds With Finite Group Action." Canadian Journal of Mathematics 45, no. 6 (December 1, 1993): 1200–1210. http://dx.doi.org/10.4153/cjm-1993-067-4.

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AbstractAn appropriate definition of equivariant formality for spaces equipped with the action of a finite group G, and for equivariant maps between such spaces, is given. Kahler manifolds with holomorphic G-actions, and equivariant holomorphic maps between such Kàhler manifolds, are proven to be equivariantly formal, generalizing results of Deligne, Griffiths, Morgan, and Sullivan

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25

Bocheński, Maciej, Piotr Jastrzębski, Takayuki Okuda, and Aleksy Tralle. "Proper SL(2, ℝ)-actions on homogeneous spaces." International Journal of Mathematics 27, no. 13 (December 2016): 1650106. http://dx.doi.org/10.1142/s0129167x16501068.

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We study the existence problem of proper actions of [Formula: see text] on homogeneous spaces [Formula: see text] of reductive type. Based on Kobayashi’s properness criterion [T. Kobayashi, Proper action on a homogeneous space of reductive type, Math. Ann. 285 (1989) 249–263.], we show that [Formula: see text] admits a proper [Formula: see text]-action via [Formula: see text] if a maximally split abelian subspace of Lie [Formula: see text] is included in the wall defined by a restricted root of Lie [Formula: see text]. We also give a number of examples of such [Formula: see text].

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26

McAvoy, Alex, and Christoph Hauert. "Autocratic strategies for iterated games with arbitrary action spaces." Proceedings of the National Academy of Sciences 113, no. 13 (March 14, 2016): 3573–78. http://dx.doi.org/10.1073/pnas.1520163113.

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The recent discovery of zero-determinant strategies for the iterated prisoner’s dilemma sparked a surge of interest in the surprising fact that a player can exert unilateral control over iterated interactions. These remarkable strategies, however, are known to exist only in games in which players choose between two alternative actions such as “cooperate” and “defect.” Here we introduce a broader class of autocratic strategies by extending zero-determinant strategies to iterated games with more general action spaces. We use the continuous donation game as an example, which represents an instance of the prisoner’s dilemma that intuitively extends to a continuous range of cooperation levels. Surprisingly, despite the fact that the opponent has infinitely many donation levels from which to choose, a player can devise an autocratic strategy to enforce a linear relationship between his or her payoff and that of the opponent even when restricting his or her actions to merely two discrete levels of cooperation. In particular, a player can use such a strategy to extort an unfair share of the payoffs from the opponent. Therefore, although the action space of the continuous donation game dwarfs that of the classic prisoner’s dilemma, players can still devise relatively simple autocratic and, in particular, extortionate strategies.

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27

Anselmi, Jonatha, François Dufour, and Tomás Prieto-Rumeau. "Computable approximations for average Markov decision processes in continuous time." Journal of Applied Probability 55, no. 2 (June 2018): 571–92. http://dx.doi.org/10.1017/jpr.2018.36.

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Abstract In this paper we study the numerical approximation of the optimal long-run average cost of a continuous-time Markov decision process, with Borel state and action spaces, and with bounded transition and reward rates. Our approach uses a suitable discretization of the state and action spaces to approximate the original control model. The approximation error for the optimal average reward is then bounded by a linear combination of coefficients related to the discretization of the state and action spaces, namely, the Wasserstein distance between an underlying probability measure μ and a measure with finite support, and the Hausdorff distance between the original and the discretized actions sets. When approximating μ with its empirical probability measure we obtain convergence in probability at an exponential rate. An application to a queueing system is presented.

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28

Garcia, J., and F. Fernandez. "Safe Exploration of State and Action Spaces in Reinforcement Learning." Journal of Artificial Intelligence Research 45 (December 19, 2012): 515–64. http://dx.doi.org/10.1613/jair.3761.

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In this paper, we consider the important problem of safe exploration in reinforcement learning. While reinforcement learning is well-suited to domains with complex transition dynamics and high-dimensional state-action spaces, an additional challenge is posed by the need for safe and efficient exploration. Traditional exploration techniques are not particularly useful for solving dangerous tasks, where the trial and error process may lead to the selection of actions whose execution in some states may result in damage to the learning system (or any other system). Consequently, when an agent begins an interaction with a dangerous and high-dimensional state-action space, an important question arises; namely, that of how to avoid (or at least minimize) damage caused by the exploration of the state-action space. We introduce the PI-SRL algorithm which safely improves suboptimal albeit robust behaviors for continuous state and action control tasks and which efficiently learns from the experience gained from the environment. We evaluate the proposed method in four complex tasks: automatic car parking, pole-balancing, helicopter hovering, and business management.

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29

Hambleton, Ian, and Ib Madsen. "Actions of Finite Groups on Rn+k with Fixed Set Rk." Canadian Journal of Mathematics 38, no. 4 (August 1, 1986): 781–860. http://dx.doi.org/10.4153/cjm-1986-041-x.

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In this paper we study the existence problem for topological actions of finite groups on euclidean spaces Rn+k which are free outside a fixed point set Rk (embedded as a vector subspace). We refer to such an action as a semi-free action on (Rn+k, Rn) and note that all our actions will be assumed orientation-preserving.Suppose the finite group π acts semi-freely on (Rn+k, Rn), then it acts freely on (Rn+k – Rn) = Sn–l × Rk+1. Since this space is homotopy equivalent to Sn–l, π will have periodic integral cohomology and n will be a multiple of the period. In fact the orbit spaceis a finitely-dominated Poincaré complex of formal dimension n – 1 with π1W = π and as considered by Swan [41].

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30

GARCÍA, ESTEBAN O., ENRIQUE MUNOZ DE COTE, and EDUARDO F. MORALES. "TRANSFER LEARNING FOR CONTINUOUS STATE AND ACTION SPACES." International Journal of Pattern Recognition and Artificial Intelligence 28, no. 07 (October 14, 2014): 1460007. http://dx.doi.org/10.1142/s0218001414600076.

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Transfer learning focuses on developing methods to reuse information gathered from a source task in order to improve the learning performance in a related task. In this work, we present a novel approach to transfer knowledge between tasks in a reinforcement learning (RL) framework with continuous states and actions, where the transition and policy functions are approximated by Gaussian processes. The novelty in the proposed approach lies in the idea of transferring information about the hyper-parameters of the state transition function from the source task, which represents qualitative knowledge about the type of transition function that the target task might have, constraining the search space and accelerating the learning process. We performed experiments on relevant tasks for RL, which show a clear improvement in the overall performance when compared to state-of-the-art reinforcement learning and transfer learning algorithms for continuous state and action spaces.

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31

Iwase, Norio, and Akira Kono. "Adjoint action of a finite loop space. II." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 4 (1999): 773–85. http://dx.doi.org/10.1017/s0308210500013135.

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Adjoint actions of compact simply connected Lie groups are studied by Kozima and the second author based on the series of studies on the classification of simple Lie groups and their cohomologies. At odd primes, the first author showed that there is a homotopy theoretic approach that will prove the results of Kozima and the second author for any 1-connected finite loop spaces. In this paper, we use the rationalization of the classifying space to compute the adjoint actions and the cohomology of classifying spaces assuming torsion free hypothesis, at the prime 2. And, by using Browder's work on the Kudo–Araki operations Q1 for homotopy commutative Hopf spaces, we show the converse for general 1-connected finite loop spaces, at the prime 2. This can be done because the inclusion j: G > BAG satisfies the homotopy commutativity for any non-homotopy commutative loop space G.

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32

Thomas, L. C., and O. J. Vrieze. "Stochastic Games with Finite State and Action Spaces." Journal of the Operational Research Society 39, no. 6 (June 1988): 612. http://dx.doi.org/10.2307/2582869.

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33

Bevan, Ann L. "Creating communicative spaces in an action research study." Nurse Researcher 21, no. 2 (November 2013): 14–17. http://dx.doi.org/10.7748/nr2013.11.21.2.14.e347.

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34

Ortega, Juan-Pablo. "The symplectic reduced spaces of a Poisson action." Comptes Rendus Mathematique 334, no. 11 (January 2002): 999–1004. http://dx.doi.org/10.1016/s1631-073x(02)02394-4.

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35

Bajoori, Elnaz, János Flesch, and Dries Vermeulen. "Perfect equilibrium in games with compact action spaces." Games and Economic Behavior 82 (November 2013): 490–502. http://dx.doi.org/10.1016/j.geb.2013.08.002.

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36

De Tré, Guy, and Wouter Van Acker. "Spaces of Information Modeling, Action, and Decision Making." Library Trends 61, no. 2 (2012): 304–24. http://dx.doi.org/10.1353/lib.2012.0043.

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37

Wu, Xinxiao, Han Wang, Cuiwei Liu, and Yunde Jia. "Cross-View Action Recognition Over Heterogeneous Feature Spaces." IEEE Transactions on Image Processing 24, no. 11 (November 2015): 4096–108. http://dx.doi.org/10.1109/tip.2015.2445293.

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38

Thomas, L. C. "Stochastic Games with Finite State and Action Spaces." Journal of the Operational Research Society 39, no. 6 (June 1988): 612. http://dx.doi.org/10.1057/jors.1988.104.

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39

Reschechtko, Sasha, Vladimir M. Zatsiorsky, and Mark L. Latash. "Stability of multifinger action in different state spaces." Journal of Neurophysiology 112, no. 12 (December 15, 2014): 3209–18. http://dx.doi.org/10.1152/jn.00395.2014.

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We investigated stability of action by a multifinger system with three methods: analysis of intertrial variance, application of transient perturbations, and analysis of the system's motion in different state spaces. The “inverse piano” device was used to apply transient (lifting-and-lowering) perturbations to individual fingers during single- and two-finger accurate force production tasks. In each trial, the perturbation was applied either to a finger explicitly involved in the task or one that was not. We hypothesized that, in one-finger tasks, task-specific stability would be observed in the redundant space of finger forces but not in the nonredundant space of finger modes (commands to explicitly involved fingers). In two-finger tasks, we expected that perturbations applied to a nontask finger would not contribute to task-specific stability in mode space. In contrast to our expectations, analyses in both force and mode spaces showed lower stability in directions that did not change total force output compared with directions that did cause changes in total force. In addition, the transient perturbations led to a significant increase in the enslaving index. We consider these results within a theoretical scheme of control with referent body configurations organized hierarchically, using multiple few-to-many mappings organized in a synergic way. The observed volatility of enslaving, greater equifinality of total force compared with elemental variables, and large magnitude of motor equivalent motion in both force and mode spaces provide support for the concept of task-specific stability of performance and the existence of multiple neural loops, which ensure this stability.

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40

Dessai, Anand. "Homotopy complex projective spaces with Pin(2)-action." Topology and its Applications 122, no. 3 (August 2002): 487–99. http://dx.doi.org/10.1016/s0166-8641(01)00192-4.

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41

Jones, P. W., and O. J. Vrieze. "Stochastic Games with Finite State and Action Spaces." Journal of the Royal Statistical Society. Series A (Statistics in Society) 151, no. 2 (1988): 384. http://dx.doi.org/10.2307/2982795.

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42

Piso, M. I. "Relativistic action over simplicial paths in Euclidean spaces." Il Nuovo Cimento B Series 11 108, no. 11 (November 1993): 1307–11. http://dx.doi.org/10.1007/bf02741282.

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43

Barthel, Anne-Christine, and Eric Hoffmann. "Comparing optimal choices with multi-dimensional action spaces." Journal of Mathematical Economics 70 (May 2017): 45–50. http://dx.doi.org/10.1016/j.jmateco.2017.01.009.

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44

Khristoforov, M., and G. Panina. "Swap action on moduli spaces of polygonal linkages." Journal of Mathematical Sciences 195, no. 2 (October 23, 2013): 237–44. http://dx.doi.org/10.1007/s10958-013-1576-2.

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45

Uc-Cetina, Víctor. "A Novel Reinforcement Learning Architecture for Continuous State and Action Spaces." Advances in Artificial Intelligence 2013 (April 18, 2013): 1–10. http://dx.doi.org/10.1155/2013/492852.

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We introduce a reinforcement learning architecture designed for problems with an infinite number of states, where each state can be seen as a vector of real numbers and with a finite number of actions, where each action requires a vector of real numbers as parameters. The main objective of this architecture is to distribute in two actors the work required to learn the final policy. One actor decides what action must be performed; meanwhile, a second actor determines the right parameters for the selected action. We tested our architecture and one algorithm based on it solving the robot dribbling problem, a challenging robot control problem taken from the RoboCup competitions. Our experimental work with three different function approximators provides enough evidence to prove that the proposed architecture can be used to implement fast, robust, and reliable reinforcement learning algorithms.

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46

DI SCALA, ANTONIO J. "POLAR ACTIONS ON BERGER SPHERES." International Journal of Geometric Methods in Modern Physics 03, no. 05n06 (September 2006): 1019–23. http://dx.doi.org/10.1142/s0219887806001466.

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The object of this article is to study a torus action on a so-called Berger sphere. We also make some comments on polar actions on naturally reductive homogeneous spaces. Finally, we prove a rigidity-type theorem for Riemannian manifolds carrying a polar action with a fix point.

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Yoshida, Masamichi. "Odometer action on Riesz product." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 61, no. 2 (October 1996): 143–49. http://dx.doi.org/10.1017/s144678870000015x.

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AbstractWe consider the Riesz product with a constant coefficient and odometer action over infinite product spaces. By studying the ratio set we can conclude the type of the above dynamical systems is III1.

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48

Yi, Inhyeop. "Continuous Orbit Equivalence on Self-Similar Graph Actions." Mathematics 7, no. 10 (October 18, 2019): 990. http://dx.doi.org/10.3390/math7100990.

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For self-similar graph actions, we show that isomorphic inverse semigroups associated to a self-similar graph action are a complete invariant for the continuous orbit equivalence of inverse semigroup actions on infinite path spaces.

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49

Delzant, Thomas, and Pierre Py. "Kähler groups, real hyperbolic spaces and the Cremona group. With an appendix by Serge Cantat." Compositio Mathematica 148, no. 1 (November 30, 2011): 153–84. http://dx.doi.org/10.1112/s0010437x11007068.

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AbstractGeneralizing a classical theorem of Carlson and Toledo, we prove thatanyZariski dense isometric action of a Kähler group on the real hyperbolic space of dimension at least three factors through a homomorphism onto a cocompact discrete subgroup of PSL2(ℝ). We also study actions of Kähler groups on infinite-dimensional real hyperbolic spaces, describe some exotic actions of PSL2(ℝ) on these spaces, and give an application to the study of the Cremona group.

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50

Lusala, Tsasa, and Jędrzej Śniatycki. "Stratified Subcartesian Spaces." Canadian Mathematical Bulletin 54, no. 4 (December 1, 2011): 693–705. http://dx.doi.org/10.4153/cmb-2011-026-3.

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AbstractWe show that if the family of orbits of all vector fields on a subcartesian space P is locally finite and each orbit in is locally closed, then defines a smooth Whitney A stratification of P. We also show that the stratification by orbit type of the space of orbits M/G of a proper action of a Lie group G on a smooth manifold M is given by orbits of the family of all vector fields on M/G.

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