Relevant bibliographies by topics / Topological chaos

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

Academic literature on the topic 'Topological chaos'

Author: Grafiati
Published: 4 June 2021
Last updated: 12 February 2022

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Journal articles on the topic "Topological chaos"

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DOWNAROWICZ, TOMASZ, and YVES LACROIX. "Measure-theoretic chaos." Ergodic Theory and Dynamical Systems 34, no. 1 (2012): 110–31. http://dx.doi.org/10.1017/etds.2012.117.

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AbstractWe define new isomorphism invariants for ergodic measure-preserving systems on standard probability spaces, called measure-theoretic chaos and measure-theoretic$^+$ chaos. These notions are analogs of the topological chaos DC2 and its slightly stronger version (which we denote by $\text {DC}1\frac 12$). We prove that: (1) if a topological system is measure-theoretically (measure-theoretically$^+$) chaotic with respect to at least one of its ergodic measures then it is topologically DC2 $(\text {DC}1\frac 12)$ chaotic; (2) every ergodic system with positive Kolmogorov–Sinai entropy is m
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Lu, Tianxiu, Peiyong Zhu, and Xinxing Wu. "The Retentivity of Chaos under Topological Conjugation." Mathematical Problems in Engineering 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/817831.

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The definitions of Devaney chaos (DevC), exact Devaney chaos (EDevC), mixing Devaney chaos (MDevC), and weak mixing Devaney chaos (WMDevC) are extended to topological spaces. This paper proves that these chaotic properties are all preserved under topological conjugation. Besides, an example is given to show that the Li-Yorke chaos is not preserved under topological conjugation if the domain is extended to a general metric space.
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Qian, Yun, and Peng Guan. "Li-York Chaos of Set-Valued Discrete Dynamical Systems Based on Semi-Group Actions." Applied Mechanics and Materials 380-384 (August 2013): 1778–82. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.1778.

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t is well known that a semi-groups action on a space could appear chaos phenomenon, like Li-York chaos and so on. Li-York chaos has important relations with topological transitivity and periodic point. This study analyzed metric space and its dinduced Hausdorff metric space. Letis a semi-group. We make continuously act on space. We study topological transitivity and betweenand. Some important results are presented which show that if is topological transitivity and periodicity (which means Li-York chaos at the same time), then the action of semi-grouponis Li-York chaos.
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Li, Shihai. "ω-Chaos and Topological Entropy". Transactions of the American Mathematical Society 339, № 1 (1993): 243. http://dx.doi.org/10.2307/2154217.

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Tomaschitz, Roman. "Topological evolution and cosmic chaos." Reports on Mathematical Physics 40, no. 2 (1997): 359–65. http://dx.doi.org/10.1016/s0034-4877(97)85933-2.

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Tan, Amanda J., Eric Roberts, Spencer A. Smith, et al. "Topological chaos in active nematics." Nature Physics 15, no. 10 (2019): 1033–39. http://dx.doi.org/10.1038/s41567-019-0600-y.

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Li, Shi Hai. "$\omega$-chaos and topological entropy." Transactions of the American Mathematical Society 339, no. 1 (1993): 243–49. http://dx.doi.org/10.1090/s0002-9947-1993-1108612-8.

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Leboeuf, P., J. Kurchan, M. Feingold, and D. P. Arovas. "Topological aspects of quantum chaos." Chaos: An Interdisciplinary Journal of Nonlinear Science 2, no. 1 (1992): 125–30. http://dx.doi.org/10.1063/1.165915.

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Liu, Xin, Huoyun Wang, and Heman Fu. "Topological Sequence Entropy and Chaos." International Journal of Bifurcation and Chaos 24, no. 07 (2014): 1450100. http://dx.doi.org/10.1142/s0218127414501004.

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A dynamical system is called a null system, if the topological sequence entropy along any strictly increasing sequence of non-negative integers is 0. Given 0 ≤ p ≤ q ≤ 1, a dynamical system is [Formula: see text] chaotic, if there is an uncountable subset in which any two different points have trajectory approaching time set with lower density p and upper density q. It shows that, for any 0 ≤ p < q ≤ 1 or p = q = 0 or p = q = 1, a dynamical system which is null and [Formula: see text] chaotic can be realized.
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CÁNOVAS, JOSE S., and MARÍA MUÑOZ. "REVISITING PARRONDO'S PARADOX FOR THE LOGISTIC FAMILY." Fluctuation and Noise Letters 12, no. 03 (2013): 1350015. http://dx.doi.org/10.1142/s0219477513500156.

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The aim of this paper is to investigate the existence of Parrondo's paradox for the logistic family fa(x) = ax(1 - x), x ∈ [0, 1], when the parameter value a ranges over the interval [1, 4]. We find that a paradox of type "order + order = chaos" arises for both physically observable and topological chaos, while a "chaos + chaos = order" paradox can be only detected for the case of physically observable chaos. In addition, we raise the question of whether the paradox "chaos + chaos = order" can appear in the topological sense or whether, as our computations seem to show, it is impossible for th
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Dissertations / Theses on the topic "Topological chaos"

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Gheisarieha, Mohsen. "Topological chaos and chaotic mixing of viscous flows." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/27768.

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Since it is difficult or impossible to generate turbulent flow in a highly viscous fluid or a microfluidic system, efficient mixing becomes a challenge. However, it is possible in a laminar flow to generate chaotic particle trajectories (well-known as chaotic advection), that can lead to effective mixing. This dissertation studies mixing in flows with the limiting case of zero Reynolds numbers that are called Stokes flows and illustrates the practical use of different theories, namely the topological chaos theory, the set-oriented analysis and lobe dynamics in the analysis, design and optimiza
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Chen, Jie. "Topological Chaos and Mixing in Lid-Driven Cavities and Rectangular Channels." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/29863.

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Fluid mixing is a challenging problem in laminar flow systems. Even in microfluidic systems, diffusion is often negligible compared to advection in the flow. The idea of chaotic advection can be applied in these systems to enhance mixing efficiency. Topological chaos can also lead to efficient and rapid mixing. In this dissertation, an approach to enhance fluid mixing in laminar flows without internal rods is demonstrated by using the idea of topological chaos. Periodic motion of three stirrers in a two-dimensional flow can lead to chaotic transport of the surrounding fluid. For certain stirr
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Kumar, Pankaj. "Chaos in Pulsed Laminar Flow." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/39260.

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Fluid mixing is a challenging problem in laminar flow systems. Chaotic advection can play an important role in enhancing mixing in such flow. In this thesis, different approaches are used to enhance fluid mixing in two laminar flow systems. In the first system, chaos is generated in a flow between two closely spaced parallel circular plates by pulsed operation of fluid extraction and reinjection through singularities in the domain. A singularity through which fluid is injected (or extracted) is called a source (or a sink). In a bounded domain, one source and one sink with equal strength operat
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Pinto, Reynaldo Daniel. "Comportamento Complexo na Experiência da Torneira Gotejante." Universidade de São Paulo, 1999. http://www.teses.usp.br/teses/disponiveis/43/43133/tde-11122013-145705/.

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Montamos um aparato experimental para o estudo de comportamentos complexos na dinâmica de formação de gotas d\'água no bico de uma torneira. Desenvolvemos um sistema hidráulico em circuito fechado, e um sistema de aquisição de dados automatizado, que também controla a abertura da torneira (uma válvula de agulha). Utilizamos como parâmetro de controle a taxa de gotejamento estabelecida pela abertura da torneira. Os dados são séries de tempos {T n} entre gotas sucessivas para cada taxa de gotejamento. Utilizando diagramas de bifurcação, e reconstruções do espaço de fase com mapas de primeiro r
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Polo, Fabrizio. "Equidistribution on Chaotic Dynamical Systems." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306527005.

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Friot, Nicolas. "Itérations chaotiques pour la sécurité de l'information dissimulée." Thesis, Besançon, 2014. http://www.theses.fr/2014BESA2035/document.

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Les systèmes dynamiques discrets, œuvrant en itérations chaotiques ou asynchrones, se sont avérés être des outils particulièrement intéressants à utiliser en sécurité informatique, grâce à leur comportement hautement imprévisible, obtenu sous certaines conditions. Ces itérations chaotiques satisfont les propriétés de chaos topologiques et peuvent être programmées de manière efficace. Dans l’état de l’art, elles ont montré tout leur intérêt au travers de schémas de tatouage numérique. Toutefois, malgré leurs multiples avantages, ces algorithmes existants ont révélé certaines limitations. Cette
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Brandão, Dienes de Lima. "Sobre o caos de Devaney e implicações /." São José do Rio Preto, 2019. http://hdl.handle.net/11449/191142.

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Orientador: Weber Flávio Pereira<br>Resumo: A Teoria dos Sistemas Dinâmicos pode ser aplicada em diversas áreas da ciência, para, por exemplo, modelar fenômenos e problemas: Biológicos, da Física, Mecânica, Eletrônica, Economia, etc. Um sistema pode ser definido como um conjunto de elementos agrupados que mantêm alguma interação, de modo que existam relações de causa e efeito. Dizemos que é dinâmico quando algumas grandezas que compõem os elementos variam no tempo, sendo o tempo discreto quando a variável tempo é um número inteiro. Na busca de uma compreensão qualitativa e/ou topológica de um s
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Huang, Po-Ying, and 黃柏穎. "Global attractor and topological chaos of second-order difference equations in discrete Hamiltonian systems." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/44498827261819052017.

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碩士<br>國立交通大學<br>應用數學系所<br>99<br>In this thesis, we discuss two distinct dynamics of the difference equation ∆[p∆x(t-1)]+qx(t)=f(x(t-1)) or f(x(t)), t∈Z, where ∆x(t-1)=ax(t)-bx(t-1). These two dynamics are the behavior of globally attracting and topological chaos. We have several results. Under some conditions of a, b, p and q, every orbit of the equation asymptotically converges to a global attractor. See theorems 2.2 and 2.3. If there exists a function relating to f which has more than one simple zeros or positive topological entropy at an expected parametric value, then the shift map restric
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Rao, Pradeep C. "Analysis of Topological Chaos in Ghost Rod Mixing at Finite Reynolds Numbers Using Spectral Methods." 2009. http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7609.

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The effect of finite Reynolds numbers on chaotic advection is investigated for two dimensional lid-driven cavity flows that exhibit topological chaos in the creeping flow regime. The emphasis in this endeavor is to study how the inertial effects present due to small, but non-zero, Reynolds number influence the efficacy of mixing. A spectral method code based on the Fourier-Chebyshev method for two-dimensional flows is developed to solve the Navier-Stokes and species transport equations. The high sensitivity to initial conditions and the exponentional growth of errors in chaotic flows necessita
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Müller-Bender, David. "Nonlinear Dynamics and Chaos in Systems with Time-Varying Delay." 2020. https://monarch.qucosa.de/id/qucosa%3A72483.

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Systeme mit Zeitverzögerung sind dadurch charakterisiert, dass deren zukünftige Entwicklung durch den Zustand zum aktuellen Zeitpunkt nicht eindeutig festgelegt ist. Die Historie des Zustands muss in einem Zeitraum bekannt sein, dessen Länge Totzeit genannt wird und die Gedächtnislänge festlegt. In dieser Arbeit werden fundamentale Effekte untersucht, die sich ergeben, wenn die Totzeit zeitlich variiert wird. Im ersten Teil werden zwei Klassen periodischer Totzeitvariationen eingeführt. Da diese von den dynamischen Eigenschaften einer eindimensionalen iterierten Abbildung abgeleitet werden, di
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Books on the topic "Topological chaos"

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Block, L. S. Dynamics in one dimension. Springer-Verlag, 1992.

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Coppel, William A., and Louis S. Block. Dynamics in One Dimension (Lecture Notes in Mathematics). Springer, 1995.

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Sethna, James P. Statistical Mechanics: Entropy, Order Parameters, and Complexity. 2nd ed. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198865247.001.0001.

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This text distills the core ideas of statistical mechanics to make room for new advances important to information theory, complexity, active matter, and dynamical systems. Chapters address random walks, equilibrium systems, entropy, free energies, quantum systems, calculation and computation, order parameters and topological defects, correlations and linear response theory, and abrupt and continuous phase transitions. Exercises explore the enormous range of phenomena where statistical mechanics provides essential insight — from card shuffling to how cells avoid errors when copying DNA, from th
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Kaloshin, Vadim, and Ke Zhang. Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202525.001.0001.

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Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. This book provides the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five
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Book chapters on the topic "Topological chaos"

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Rodrigues, Ana. "Topological theory of chaos." In One-Dimensional Dynamical Systems. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003144618-5.

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Akhmet, Marat, Mehmet Onur Fen, and Ejaily Milad Alejaily. "Unpredictability in Topological Dynamics." In Dynamics with Chaos and Fractals. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35854-9_5.

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Cattaneo, G., E. Formenti, and L. Margara. "Topological Definitions of Deterministic Chaos." In Cellular Automata. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9153-9_8.

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Tufillaro, Nicholas B. "Topological Organization of (Low-Dimensional) Chaos." In From Statistical Physics to Statistical Inference and Back. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1068-6_20.

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Cattaneo, Gianpiero, Michele Finelli, and Luciano Margara. "Topological chaos for elementary cellular automata." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-62592-5_76.

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Aranson, I. "Topological Defects and Control of Spatio-Temporal Chaos." In Handbook of Chaos Control. Wiley-VCH Verlag GmbH & Co. KGaA, 2006. http://dx.doi.org/10.1002/3527607455.ch5.

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Bajer, K., and H. K. Moffatt. "Chaos Associated with Fluid Inertia." In Topological Aspects of the Dynamics of Fluids and Plasmas. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-017-3550-6_31.

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Toda, Mikito. "A Topological Approach to Phase of Quantum Chaos." In Quantum Communication, Computing, and Measurement. Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-5923-8_35.

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Cattaneo, Gianpiero, and Luciano Margara. "Topological definitions of chaos applied to cellular automata dynamics." In Mathematical Foundations of Computer Science 1998. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0055833.

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Niculescu, Constantin P. "Topological Transitivity and Recurrence as a Source of Chaos." In Functional Analysis and Economic Theory. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-72222-6_9.

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Conference papers on the topic "Topological chaos"

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Ezersky, A. B. "The Dynamics of Bound States of Topological Defects in Extended Spatially Periodic Structures." In EXPERIMENTAL CHAOS: 6th Experimental Chaos Conference. AIP, 2002. http://dx.doi.org/10.1063/1.1487554.

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Amon, Axelle. "Topological signature of deterministic chaos in short nonstationary signals from an optical parametric oscillator." In EXPERIMENTAL CHAOS: 8th Experimental Chaos Conference. AIP, 2004. http://dx.doi.org/10.1063/1.1846498.

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Jin, Weifeng, Fangyue Chen, and Chunlan Yang. "Topological Chaos of Cellular Automata Rules." In 2009 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2009. http://dx.doi.org/10.1109/iwcfta.2009.52.

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Raymond, Laurent, Alberto D. Verga, and Arnaud Demion. "Magnetic Impurities and Transport in Topological Insulators." In Conference on Chaos, Complexity and Transport 2015. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813202740_0013.

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REYES, M. B., and J. C. SARTORELLI. "TOPOLOGICAL ANALYSIS IN A DRIPPING FAUCET EXPERIMENT." In Space-Time Chaos: Characterization, Control and Synchronization. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811660_0013.

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Afenchenko, V. O., A. B. Ezersky, and S. V. Kiyashko. "Controlling spatio-temporal chaos of topological defects." In SPIE Proceedings, edited by Alexander M. Sergeev. SPIE, 2006. http://dx.doi.org/10.1117/12.675579.

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Guan, Junbiao, and Shaowei Shen. "Topological Conjugacy Classification of Cellular Automata." In 2009 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2009. http://dx.doi.org/10.1109/iwcfta.2009.51.

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Guyeux, Christophe, and Jacques M. Bahi. "Topological chaos and chaotic iterations application to hash functions." In 2010 International Joint Conference on Neural Networks (IJCNN). IEEE, 2010. http://dx.doi.org/10.1109/ijcnn.2010.5596512.

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Galias, Zbigniew. "Topological chaos in the parallel inductor-capacitor-memristor circuit." In 2016 International Conference on Signals and Electronic Systems (ICSES). IEEE, 2016. http://dx.doi.org/10.1109/icses.2016.7593838.

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Zhanjiang, Ji, Qin Guijiang, and Zhai Cong. "Chain Recurrent Point and Devaney Chaos of Topological Groups." In 2018 3rd International Conference on Smart City and Systems Engineering (ICSCSE). IEEE, 2018. http://dx.doi.org/10.1109/icscse.2018.00184.

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