Decay of correlation implies chaos in the sense of Devaney

DOI10.1016/j.chaos.2004.01.006zbMath1060.37002OpenAlexW2045412537MaRDI QIDQ1766627

Wei Lin, Zhengjie Xu, Jiong Ruan

Publication date: 8 March 2005

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2004.01.006

zbMATH Keywords

stochastic dynamicssymbolic dynamicschaos in the sense of Devaneytransformation map

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (19)

The central limit theorem and chaos ⋮ Strong sensitivity of systems satisfying the large deviations theorem ⋮ Are there chaotic maps in the sphere? ⋮ The large deviations theorem and sensitivity ⋮ On the Large Deviations Theorem of Weaker Types ⋮ On the large deviations theorem and ergodicity ⋮ A note on shadowing with chain transitivity ⋮ A note on stronger forms of sensitivity for dynamical systems ⋮ Central limit theorem and chaoticity ⋮ Stochastic properties in Devaney's chaos ⋮ On some stochastic properties in Devaney's chaos ⋮ On mixing property in set-valued discrete systems ⋮ The central limit theorem and ergodicity ⋮ Sensitivity and Transitivity of Systems Satisfying the Large Deviations Theorem in a Sequence ⋮ A note on decay of correlation implies chaos in the sense of Devaney ⋮ Study on Strong Sensitivity of Systems Satisfying the Large Deviations Theorem ⋮ On the Iteration Properties of Large Deviations Theorem ⋮ A note on stronger forms of sensitivity for inverse limit dynamical systems ⋮ The large deviations theorem and ergodicity

Cites Work

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• On Devaney's Definition of Chaos
• Period Three Implies Chaos
• Ergodic Transformations from an Interval Into Itself
• On Intervals, Transitivity = Choas
• Chaotic dynamics of an integrate-and-fire circuit with periodic pulse-train input

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