Weak-mixing implies sensitive dependence

DOI10.1016/j.jmaa.2004.06.066zbMath1057.28008OpenAlexW2040161418MaRDI QIDQ1766737

Xinhua Yan, Ling-Shu Wang, LianFa He

Publication date: 8 March 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.06.066

zbMATH Keywords

measure-preserving mapsensitive dependenceweak-mixingmeasure-preserving semi-flow

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodicity, mixing, rates of mixing (37A25)

Related Items (26)

Several sufficient conditions for sensitive dependence on initial conditions ⋮ On Measure Chaotic Dynamical Systems ⋮ Erratum to ``A note on uniform convergence and transitivity ⋮ Sensitivity of iterated function systems under the product operation ⋮ Three types of distributional chaos for a sequence of uniformly convergent continuous maps ⋮ On Weak Lyapunov Exponent and Sensitive Dependence of Interval Maps ⋮ Relationships among some chaotic properties of non-autonomous discrete dynamical systems ⋮ Sensitivity for topologically double ergodic dynamical systems ⋮ 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 ⋮ A note on uniform convergence and transitivity ⋮ Measurable sensitivity ⋮ Stronger forms of sensitivity for measure-preserving maps and semiflows on probability spaces ⋮ F-sensitivity and (F_1, F_2)-sensitivity between dynamical systems and their induced hyperspace dynamical systems ⋮ Sufficient conditions for ergodic sensitivity ⋮ Furstenberg families and chaos on uniform limit maps ⋮ Several sufficient conditions for a map and a semi-flow to be ergodically sensitive ⋮ Central limit theorem and chaoticity ⋮ Unnamed Item ⋮ Sensitivity and Transitivity of Systems Satisfying the Large Deviations Theorem in a Sequence ⋮ Study on Strong Sensitivity of Systems Satisfying the Large Deviations Theorem ⋮ A note on stronger forms of sensitivity for inverse limit dynamical systems ⋮ On Li-Yorke measurable sensitivity ⋮ Sensitivity of non-autonomous discrete dynamical systems

Cites Work

• Chaotic properties of mappings on a probability space.
• Everywhere chaotic homeomorphisms on manifolds and \(k\)-dimensional Menger manifolds
• On Devaney's Definition of Chaos
• Sensitive dependence on initial conditions
• Unnamed Item
• Unnamed Item

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