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Journal of Difference Equations and Applications Volume 15, 2009 - Issue 1: Combinatorial and Topological Dynamics
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Original Articles

Topological chaos: what may this mean?

François Blanchard Laboratoire d'Analyse et de Mathématiques Appliquées, CNRS-U. de Marne-la-Vallée, Marne-la-Vallée Cedex 2, FranceCorrespondence[email protected]
Pages 23-46 | Received 30 Jul 2008, Accepted 02 Aug 2008, Published online: 02 Dec 2008

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Yingxuan Niu. (2017) The average shadowing property and chaos for continuous flows. Journal of Dynamical Systems and Geometric Theories 15:2, pages 99-109.
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T.K. Subrahmonian Moothathu. (2015) Remarks on the three ingredients of chaos. Journal of Difference Equations and Applications 21:7, pages 579-591.
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Liuchun Deng, M. Ali Khan & Tapan Mitra. (2022) Continuous unimodal maps in economic dynamics: On easily verifiable conditions for topological chaos. Journal of Economic Theory 201, pages 105446.
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Ryszard J. Pawlak. (2022) Chaotic Points of Multifunctions. Taiwanese Journal of Mathematics -1:-1.
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V. A. Khodel, J. W. Clark & M. V. Zverev. (2020) Topological disorder triggered by interaction-induced flattening of electron spectra in solids. Physical Review B 102:20.
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Thomas M. Kwok, Zheng Li, Ruxu Du & Guanrong Chen. (2019) Modeling and Experimental Validation of the Chaotic Behavior of a Robot Whip. Journal of Mechanics 36:3, pages 373-394.
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Renwei Kang, Junfeng Wang, Jianfeng Cheng, Jianqiu Chen & Yanzhi Pang. (2019) Intelligent Forecasting of Automatic Train Protection System Failure Rate in China High-speed Railway. Eksploatacja i Niezawodność – Maintenance and Reliability 21:4, pages 567-576.
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RYSZARD J. PAWLAK & JUSTYNA POPRAWA. (2019) ON GENERATORS AND DISTURBANCES OF DYNAMICAL SYSTEMS IN THE CONTEXT OF CHAOTIC POINTS. Bulletin of the Australian Mathematical Society 100:1, pages 76-85.
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Seyyed Alireza Ahmadi, Xinxing Wu, Zonghong Feng, Xin Ma & Tianxiu Lu. (2018) On the Entropy Points and Shadowing in Uniform Spaces. International Journal of Bifurcation and Chaos 28:12, pages 1850155.
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Alessandro Fedeli. (2018) Topologically sensitive dynamical systems. Topology and its Applications 248, pages 192-203.
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Ekta Shah. (2018) Devaney's Chaos for Maps on $G$-spaces. Taiwanese Journal of Mathematics 22:2.
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ANNA LORANTY & RYSZARD J. PAWLAK. (2017) ON FUNCTIONS ATTRACTING POSITIVE ENTROPY. Bulletin of the Australian Mathematical Society 97:1, pages 69-79.
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Ryszard J. Pawlak. (2018) Distortion of Dynamical Systems in the Context of Focusing the Chaos Around the Point. International Journal of Bifurcation and Chaos 28:01, pages 1850006.
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Jian Li & Xiang Dong Ye. (2015) Recent development of chaos theory in topological dynamics. Acta Mathematica Sinica, English Series 32:1, pages 83-114.
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Lei Liu, Haitao Li & Jinli Pang. (2015) On local aspects of sensitivity in topological dynamics. Advances in Difference Equations 2015:1.
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Jorge Duarte, Carla Rodrigues, Cristina Janu?rio, Nuno Martins & Josep Sardany?s. (2015) How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?. Acta Biotheoretica 63:4, pages 341-361.
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Jian Li, Dominik Kwietniak, Marcin Kulczycki & Fryderyk Falniowski. (2015) Two results on entropy, chaos and independence in symbolic dynamics. Discrete and Continuous Dynamical Systems - Series B 20:10, pages 3487-3505.
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Jarkko Kari & Siamak Taati. (2015) Statistical Mechanics of Surjective Cellular Automata. Journal of Statistical Physics 160:5, pages 1198-1243.
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Viorel Nitica & Andrei Török. (2015) Open and Dense Topological Transitivity of Extensions by Non-Compact Fiber of Hyperbolic Systems: A Review. Axioms 4:1, pages 84-101.
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Lei Liu & Yuejuan Sun. (2014) Weakly mixing sets and transitive sets for non-autonomous discrete systems. Advances in Difference Equations 2014:1.
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GRZEGORZ HARAŃCZYK, DOMINIK KWIETNIAK & PIOTR OPROCHA. (2013) Topological structure and entropy of mixing graph maps. Ergodic Theory and Dynamical Systems 34:5, pages 1587-1614.
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Piotr Oprocha & Guohua Zhang. 2014. Recent Progress in General Topology III. Recent Progress in General Topology III 665 709 .
Emma D?Aniello & Timothy Steele. (2014) Chaotic behaviour of the map x ? ?(x, f). Open Mathematics 12:4.
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Lei Liu. (2013) On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete Systems. Discrete Dynamics in Nature and Society 2013, pages 1-6.
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V. Berth?. (2011) Numeration and discrete dynamical systems. Computing 94:2-4, pages 369-387.
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Josep Sardanyés, Jorge Duarte, Cristina Januário & Nuno Martins. (2012) Topological entropy of catalytic sets: Hypercycles revisited. Communications in Nonlinear Science and Numerical Simulation 17:2, pages 795-803.
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Piotr Oprocha & Paweł Wilczyński. (2010) Topological entropy for local processes. Journal of Differential Equations 249:8, pages 1929-1967.
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Jorge Duarte, Cristina Januário, Nuno Martins & Josep Sardanyés. (2010) Quantifying chaos for ecological stoichiometry. Chaos: An Interdisciplinary Journal of Nonlinear Science 20:3.
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Jorge Duarte, Cristina Januário, Nuno Martins & Josep Sardanyés. (2009) Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach. Chaos: An Interdisciplinary Journal of Nonlinear Science 19:4.
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