Relevant bibliographies by topics / Ergodic and geometric group theory

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Ergodic and geometric group theory'

Author: Grafiati
Published: 31 August 2024
Last updated: 31 July 2025

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Journal articles on the topic "Ergodic and geometric group theory"

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Skripchenko, Alexandra Sergeevna. "Renormalization in one-dimensional dynamics." Russian Mathematical Surveys 78, no. 6 (2023): 983–1021. http://dx.doi.org/10.4213/rm10110e.

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The study of the dynamical and topological properties of interval exchange transformations and their natural generalizations is an important problem, which lies at the intersection of several branches of mathematics, including dynamical systems, low-dimensional topology, algebraic geometry, number theory, and geometric group theory. The purpose of the survey is to make a systematic presentation of the existing results on the ergodic and geometric characteristics of the one-dimensional maps under consideration, as well as on the measured foliations on surfaces and two-dimensional complexes that
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Hartman, Yair, and Ariel Yadin. "Furstenberg entropy of intersectional invariant random subgroups." Compositio Mathematica 154, no. 10 (2018): 2239–65. http://dx.doi.org/10.1112/s0010437x18007261.

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We study the Furstenberg-entropy realization problem for stationary actions. It is shown that for finitely supported probability measures on free groups, any a priori possible entropy value can be realized as the entropy of an ergodic stationary action. This generalizes results of Bowen. The stationary actions we construct arise via invariant random subgroups (IRSs), based on ideas of Bowen and Kaimanovich. We provide a general framework for constructing a continuum of ergodic IRSs for a discrete group under some algebraic conditions, which gives a continuum of entropy values. Our tools apply,
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Guirardel, Vincent, Camille Horbez, and Jean Lécureux. "Cocycle superrigidity from higher rank lattices to $ {{\rm{Out}}}{(F_N)} $." Journal of Modern Dynamics 18 (2022): 291. http://dx.doi.org/10.3934/jmd.2022010.

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<p style='text-indent:20px;'>We prove a rigidity result for cocycles from higher rank lattices to <inline-formula><tex-math id="M2">\begin{document}$ \mathrm{Out}(F_N) $\end{document}</tex-math></inline-formula> and more generally to the outer automorphism group of a torsion-free hyperbolic group. More precisely, let <inline-formula><tex-math id="M3">\begin{document}$ G $\end{document}</tex-math></inline-formula> be either a product of connected higher rank simple algebraic groups over local fields, or a lattice in such a product. Let <i
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Kida, Yoshikata. "Ergodic group theory." Sugaku Expositions 35, no. 1 (2022): 103–26. http://dx.doi.org/10.1090/suga/470.

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Young, Lai-Sang. "Geometric and Ergodic Theory of Hyperbolic Dynamical Systems." Current Developments in Mathematics 1998, no. 1 (1998): 237–78. http://dx.doi.org/10.4310/cdm.1998.v1998.n1.a6.

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Orponen, Tuomas, Pablo Shmerkin, and Hong Wang. "Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory." Oberwolfach Reports 20, no. 2 (2023): 1397–452. http://dx.doi.org/10.4171/owr/2023/25.

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BOWEN, LEWIS, and AMOS NEVO. "Hyperbolic geometry and pointwise ergodic theorems." Ergodic Theory and Dynamical Systems 39, no. 10 (2017): 2689–716. http://dx.doi.org/10.1017/etds.2017.128.

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We establish pointwise ergodic theorems for a large class of natural averages on simple Lie groups of real rank one, going well beyond the radial case considered previously. The proof is based on a new approach to pointwise ergodic theorems, which is independent of spectral theory. Instead, the main new ingredient is the use of direct geometric arguments in hyperbolic space.
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Ziegler, Tamar. "An application of ergodic theory to a problem in geometric ramsey theory." Israel Journal of Mathematics 114, no. 1 (1999): 271–88. http://dx.doi.org/10.1007/bf02785583.

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BESSA, MÁRIO, and JORGE ROCHA. "Contributions to the geometric and ergodic theory of conservative flows." Ergodic Theory and Dynamical Systems 33, no. 6 (2012): 1709–31. http://dx.doi.org/10.1017/etds.2012.110.

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AbstractWe prove the following dichotomy for vector fields in a $C^1$-residual subset of volume-preserving flows: for Lebesgue-almost every point, either all of its Lyapunov exponents are equal to zero or its orbit has a dominated splitting. Moreover, we prove that a volume-preserving and $C^1$-stably ergodic flow can be $C^1$-approximated by another volume-preserving flow which is non-uniformly hyperbolic.
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Clay, Matt. "Geometric Group Theory." Notices of the American Mathematical Society 69, no. 10 (2022): 1. http://dx.doi.org/10.1090/noti2572.

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Dissertations / Theses on the topic "Ergodic and geometric group theory"

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Cannizzo, Jan. "Schreier Graphs and Ergodic Properties of Boundary Actions." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31444.

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This thesis is broadly concerned with two problems: investigating the ergodic properties of boundary actions, and investigating various properties of Schreier graphs. Our main result concerning the former problem is that, in a variety of situations, the action of an invariant random subgroup of a group G on a boundary of G (e.g. the hyperbolic boundary, or the Poisson boundary) is conservative (there are no wandering sets). This addresses a question asked by Grigorchuk, Kaimanovich, and Nagnibeda and establishes a connection between invariant random subgroups and normal subgroups. We approach
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Long, Yusen. "Diverse aspects of hyperbolic geometry and group dynamics." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM016.

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Cette thèse explore divers sujets liés à la géométrie hyperbolique et à la dynamique de groupes, dans le but d'étudier l'interaction entre la géométrie et la théorie de groupes. Elle couvre un large éventail de disciplines mathématiques, telles que la géométrie convexe, l'analyse stochastique, la théorie ergodiques et géométriques de groupes, et la topologie en basses dimensions, et cætera. Comme résultats de recherche, la géométrie hyperbolique des corps convexes en dimension infinie est examinée en profondeur, et des tentatives sont faites pour développer la géométrie intégrale en dimension
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Benson, Martin. "Topics in geometric group theory." Thesis, University of Nottingham, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.428957.

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Williams, Benjamin Thomas. "Two topics in geometric group theory." Thesis, University of Southampton, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323942.

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Isenrich, Claudio Llosa. "Kähler groups and Geometric Group Theory." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:4a7ab097-4de5-4b72-8fd6-41ff8861ffae.

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In this thesis we study Kähler groups and their connections to Geometric Group Theory. This work presents substantial progress on three central questions in the field: (1) Which subgroups of direct products of surface groups are Kähler? (2) Which Kähler groups admit a classifying space with finite (n-1)-skeleton but no classifying space with finitely many n-cells? (3) Is it possible to give explicit finite presentations for any of the groups constructed in response to Question 2? Question 1 was raised by Delzant and Gromov. Question 2 is intimately related to Question 1: the non-trivial exa
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Ashdown, M. A. J. "Geometric algebra, group theory and theoretical physics." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596181.

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This dissertation applies the language of geometric algebra to group theory and theoretical physics. Geometric algebra, which is introduced in Chapter 2, provides a natural extension of the concept of multiplication from real numbers to geometric objects such as line segments and planes. It is based on Clifford algebra and augmented by auxiliary definitions which give it a geometric interpretation. Since geometric algebra provides a natural encoding of the concepts of directed quantities, it has the potential to unify many of the disparate systems of notation that are used in mathematics. In C
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Gill, Olivia Jo. "Geometric and homological methods in group theory : constructing small group resolutions." Thesis, London Metropolitan University, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.573402.

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Given two groups K and H for which we have the free crossed resolutions, B* ɛ K and C* ɛ H respectively. Our aim is to construct a free crossed resolution, A* ɛ G, by way of induction on the degree n, for any semidirect product G = K ><I H. First we show how to find a set ZI of generators for the free group Al and the corresponding unique epimorphism from the free group on those generators to the semidirect product. This gives us the l-dimensional free crossed resolution A1 ɛ G, (see Proposition 4.1). Next we define a set of generators Z2 that together with Z1, constitute a gener- ating se
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Joubert, Paul. "Geometric actions of the absolute Galois group." Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/2508.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2006.<br>This thesis gives an introduction to some of the ideas originating from A. Grothendieck's 1984 manuscript Esquisse d'un programme. Most of these ideas are related to a new geometric approach to studying the absolute Galois group over the rationals by considering its action on certain geometric objects such as dessins d'enfants (called stick figures in this thesis) and the fundamental groups of certain moduli spaces of curves. I start by defining stick figures and explaining the connection between these innocent combinatoria
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El-Mosalamy, Mohamed Soliman Hassan. "Applications of star complexes in group theory." Thesis, University of Glasgow, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293464.

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Fennessey, Eric James. "Some applications of geometric techniques in combinatorial group theory." Thesis, University of Glasgow, 1989. http://theses.gla.ac.uk/6159/.

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Combinatorial group theory abounds with geometrical techniques. In this thesis we apply some of them to three distinct areas. In Chapter 1 we present all of the techniques and background material neccessary to read chapters 2,3,4. We begin by defining complexes with involutary edges and define coverings of these. We then discuss equivalences between complexes and use these in §§1.3 and 1.4 to give a way (the level method) of simplifying complexes and an application of this method (Theorem 1.3). We then discuss star-complexes of complexes. Next we present background material on diagrams and pic
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Books on the topic "Ergodic and geometric group theory"

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Koli︠a︡da, S. F. Dynamics and numbers: A special program, June 1-July 31, 2014, Max Planck Institute for Mathematics, Bonn, Germany : international conference, July 21-25, 2014, Max Planck Institute for Mathematics, Bonn, Germany. Edited by Max-Planck-Institut für Mathematik. American Mathematical Society, 2016.

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Burger, Marc. Rigidity in Dynamics and Geometry: Contributions from the Programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Institute for the Mathematical Sciences Cambridge, United Kingdom, 5 January - 7 July 2000. Springer Berlin Heidelberg, 2002.

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Bhattacharya, Siddhartha, Tarun Das, Anish Ghosh, and Riddhi Shah. Recent trends in ergodic theory and dynamical systems: International conference in honor of S.G. Dani's 65th birthday, December 26--29, 2012, Vadodara, India. American Mathematical Society, 2015.

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Bestvina, Mladen, Michah Sageev, and Karen Vogtmann. Geometric group theory. American Mathematical Society, 2014.

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Charney, Ruth, Michael Davis, and Michael Shapiro, eds. Geometric Group Theory. DE GRUYTER, 1995. http://dx.doi.org/10.1515/9783110810820.

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Arzhantseva, Goulnara N., José Burillo, Laurent Bartholdi, and Enric Ventura, eds. Geometric Group Theory. Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8412-8.

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Löh, Clara. Geometric Group Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-72254-2.

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Dani, S. G., and Anish Ghosh, eds. Geometric and Ergodic Aspects of Group Actions. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0683-3.

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Zimmer, Robert J. Ergodic theory, groups, and geometry. American Mathematical Society, 2008.

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Doran, Robert S., Calvin C. Moore, and Robert J. Zimmer, eds. Group Representations, Ergodic Theory, and Mathematical Physics. American Mathematical Society, 2008. http://dx.doi.org/10.1090/conm/449.

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Book chapters on the topic "Ergodic and geometric group theory"

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Polterovich, Leonid. "An Application to Ergodic Theory." In The Geometry of the Group of Symplectic Diffeomorphism. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8299-6_11.

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Lyndon, Roger C., and Paul E. Schupp. "Geometric Methods." In Combinatorial Group Theory. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-61896-3_3.

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Löh, Clara. "Group actions." In Geometric Group Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-72254-2_4.

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Guirardel, Vincent. "Geometric small cancellation." In Geometric Group Theory. American Mathematical Society, 2014. http://dx.doi.org/10.1090/pcms/021/03.

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Baumgartner, Udo. "Totally Disconnected, Locally Compact Groups as Geometric Objects." In Geometric Group Theory. Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8412-8_1.

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Miasnikov, Alexei, Enric Ventura, and Pascal Weil. "Algebraic Extensions in Free Groups." In Geometric Group Theory. Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8412-8_12.

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Ceccherini-Silberstein, Tullio, and Michel Coornaert. "On the Surjunctivity of Artinian Linear Cellular Automata over Residually Finite Groups." In Geometric Group Theory. Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8412-8_3.

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de Cornulier, Yves, and Avinoam Mann. "Some Residually Finite Groups Satisfying Laws." In Geometric Group Theory. Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8412-8_4.

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de Cornulier, Yves, and Pierre de la Harpe. "Décompositions de Groupes par Produit Direct et Groupes de Coxeter." In Geometric Group Theory. Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8412-8_7.

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Houcine, Abderezak Ould. "Limit Groups of Equationally Noetherian Groups." In Geometric Group Theory. Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8412-8_8.

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Conference papers on the topic "Ergodic and geometric group theory"

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Ruelle, David. "Ergodic Theory of Chaos." In Optical Bistability. Optica Publishing Group, 1985. http://dx.doi.org/10.1364/obi.1985.wc1.

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Determinsistic chaos arises in a variety of nonlinear dynamical systems in physics, and in particular in optics. One has now gained a reasonable understanding of the onset of chaos in terms of the geometry of bifurcations and strange attractors. This geometric approach does not work for attractors of more than two or three dimensions. For these, however, ergodic theory provides new concepts: characteristic exponents, entropy, information dimension, which are reproducibly estimated from physical experiments. The Characteristic exponents measure the rate of divergence of nearby trajectories of a
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Berendsohn, Benjamin Aram, and Laszlo Kozma. "Group Testing with Geometric Ranges." In 2022 IEEE International Symposium on Information Theory (ISIT). IEEE, 2022. http://dx.doi.org/10.1109/isit50566.2022.9834574.

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BOEIRA DORNELAS, BIANCA, and FRANCESCO MATUCCI. "Introduction to Combinatorial and Geometric Group Theory." In XXV Congresso de Iniciação Cientifica da Unicamp. Galoa, 2017. http://dx.doi.org/10.19146/pibic-2017-79172.

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Ruiz S., Oscar E., and Placid M. Ferreira. "Algebraic geometry and group theory in geometric constraint satisfaction." In the international symposium. ACM Press, 1994. http://dx.doi.org/10.1145/190347.190421.

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Wolf, Kurt Bernardo. "Introduction to Lie geometric optics." In The XXX Latin American school of physics ELAF: Group theory and its applications. AIP, 1996. http://dx.doi.org/10.1063/1.50229.

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Peng, Bo. "An approach to group decision making based on interval-valued intuitionistic fuzzy geometric distance measures." In 2015 International Conference on Fuzzy Theory and Its Applications (iFUZZY). IEEE, 2015. http://dx.doi.org/10.1109/ifuzzy.2015.7391901.

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Clayton, John D. "Shock compression of metal single crystals modeled via Finsler-geometric continuum theory." In SHOCK COMPRESSION OF CONDENSED MATTER - 2017: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter. Author(s), 2018. http://dx.doi.org/10.1063/1.5045034.

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Gou, J. B., Y. X. Chu, H. Wu, and Z. X. Li. "A Geometric Theory for Formulation of Form, Profile and Orientation Tolerances: Problem Formulation." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/dfm-5743.

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Abstract This paper develops a geometric theory which unifies the formulation and evaluation of form (straightness, flatness, cylindricity and circularity), profile and orientation tolerances stipulated in ANSI Y14.5M standard. In the paper, based on an an important observation that a toleranced feature exhibits a symmetry subgroup G0 under the action of the Euclidean group, SE(3), we identify the configuration space of a toleranced (or a symmetric) feature with the homogeneous space SE(3)/G0 of the Euclidean group. Geometric properties of SE(3)/G0, especially its exponential coordinates carri
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Jung, Tae-Hwa, and Changhoon Lee. "Supercritical Group Velocity for Dissipative Waves in Shallow Water." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83279.

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The group velocity for waves with energy dissipation in shallow water was investigated. In the Eulerian viewpoint, the geometric optics approach was used to get, at the first order, complex-valued wave numbers from given real-valued angular frequency, water depth, and damping coefficient. The phase velocity was obtained as the ratio of angular frequency to realvalued wave number. Then, at the second order, we obtained the energy transport equation which gives the group velocity. We also used the Lagrangian geometric optics approach which gives complex-valued angular frequencies from real-value
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Li, Z. X., B. Kang, J. B. Gou, Y. X. Chu, and M. Yeung. "Fundamentals of Workpiece Localization: Theory and Algorithms." In ASME 1996 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/imece1996-0811.

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Abstract In this paper, we present an algebraic algorithm for workpiece localization. First, we formulate the problem as a least-square problem in the configuration space Q = SE(3) × ℝ3n, where SE(3) is the Euclidean group, and n is the number of measurement points to be matched by corresponding home surface points of the workpiece. Then, we use the geometric properties of the Euclidean group to compute for the critical points of the objective function. Doing so we derive an algebraic formula for the optimal Euclidean transformation in terms of the measurement points and the corresponding home
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