On the Iteration Properties of Large Deviations Theorem

DOI10.1142/S0218127416500541zbMath1336.37008OpenAlexW2333637142MaRDI QIDQ2806176

Xinxing Wu, Xiong Wang

Publication date: 17 May 2016

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127416500541

zbMATH Keywords

ergodicitylarge deviations theorem

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25)

Related Items (22)

Weakly mixing property and chaos ⋮ The chain properties and average shadowing property of iterated function systems ⋮ Characterizing ergodicity of induced hyperspace dynamical systems ⋮ Chaos of Transformations Induced Onto the Space of Probability Measures ⋮ Topological Dynamics of Zadeh’s Extension on Upper Semi-Continuous Fuzzy Sets ⋮ A Remark on Topological Sequence Entropy ⋮ Chaos to Multiple Mappings ⋮ On the Large Deviations Theorem of Weaker Types ⋮ Shifts, rotations and distributional chaos ⋮ Topological Entropy and Mixing Invariant Extremal Distributional Chaos ⋮ Chaos in a topologically transitive semi-flow ⋮ Sufficient conditions for ergodic sensitivity ⋮ Spatio-temporal chaos in duopoly games ⋮ Chaos for finitely generated semigroup actions ⋮ A quantitative approach to syndetic transitivity and topological ergodicity ⋮ FURTHER DISCUSSION ON KATO'S CHAOS IN SET-VALUED DISCRETE SYSTEMS ⋮ Sensitivity of non-autonomous discrete dynamical systems revisited ⋮ On the iteration invariance of distributional chaos of type \(2\frac{1}{2}\) in non-autonomous discrete system ⋮ Sensitivity and Transitivity of Systems Satisfying the Large Deviations Theorem in a Sequence ⋮ Study on Strong Sensitivity of Systems Satisfying the Large Deviations Theorem ⋮ Sensitivity and transitivity of fuzzified dynamical systems ⋮ Average Shadowing Property and Asymptotic Average Shadowing Property of Linear Dynamical Systems

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• Sequence mixing and \(\alpha\)-mixing
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• Decay of correlation implies chaos in the sense of Devaney
• The large deviations theorem and ergodic sensitivity
• Central limit theorem and chaoticity
• \(\mathcal{F}\)-sensitivity and multi-sensitivity of hyperspatial dynamical systems
• On some stochastic properties in Devaney's chaos
• On mixing and partial mixing
• On various definitions of shadowing with average error in tracing
• IP-systems in ergodic theory
• On the mean ergodic theorem for subsequences
• Some Invariant σ-Algebras for Measure-Preserving Transformations

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