Transitivity, mixing and chaos for a class of set-valued mappings

DOI10.1007/S11425-004-5234-5zbMath1193.37023OpenAlexW1913407073MaRDI QIDQ854627

Yucheng Zhang, Gongfu Liao, Lidong Wang

Publication date: 6 December 2006

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-004-5234-5

Mathematics Subject Classification ID

Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (24)

Weak stability of non-autonomous discrete dynamical systems ⋮ Unnamed Item ⋮ Chaos for discrete dynamical system ⋮ Difference between Devaney chaos associated with two systems ⋮ The set-valued mapping induced by a non-minimal transitive system is Li-Yorke chaotic ⋮ Characterizing ergodicity of induced hyperspace dynamical systems ⋮ Topologically transitive and mixing properties of set-valued dynamical systems ⋮ Set-valued chaos in linear dynamics ⋮ Chaos of Transformations Induced Onto the Space of Probability Measures ⋮ Topological Dynamics of Zadeh’s Extension on Upper Semi-Continuous Fuzzy Sets ⋮ Transitive points in CR-dynamical systems ⋮ A note on shadowing with chain transitivity ⋮ Further discussion about transitivity and mixing of continuous maps on compact metric spaces ⋮ F-sensitivity and (F_1, F_2)-sensitivity between dynamical systems and their induced hyperspace dynamical systems ⋮ Characterizing mixing, weak mixing and transitivity of induced hyperspace dynamical systems ⋮ Inducing Sensitivity of Fuzzified Dynamical Systems ⋮ Sensitive dependence on initial conditions between dynamical systems and their induced hyperspace dynamical systems ⋮ Sensitivity and transitivity of fuzzified dynamical systems ⋮ Sensitivity for set-valued maps induced by \(M\)-systems ⋮ The transitivity of induced maps ⋮ Thickly syndetical sensitivity of topological dynamical system ⋮ 2-cocycles of original deformative Schrödinger-Virasoro algebras ⋮ Sensitivity of set-valued discrete systems ⋮ \(\mathcal{F}\)-sensitivity and multi-sensitivity of hyperspatial dynamical systems

Cites Work

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• Chaos caused by a strong-mixing measure-preserving transformation
• A note on transitivity in set-valued discrete systems.
• On chaotic set-valued discrete dynamical systems
• Attractors of a randomly forced electronic oscillator.
• Conley index for discrete multi-valued dynamical systems
• Chaos in a topologically transitive system
• On Devaney's Definition of Chaos
• On Intervals, Transitivity = Choas
• Devaney’s chaos implies existence of 𝑠-scrambled sets
• Chaos, Periodicity, and Snakelike Continua
• Devaney's chaos or 2-scattering implies Li-Yorke's chaos

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