Individual chaos implies collective chaos for weakly mixing discrete dynamical systems

DOI10.1016/j.chaos.2005.11.002zbMath1139.37010OpenAlexW2034508446MaRDI QIDQ2482407

Lidong Wang, Gongfu Liao, Xian-Feng Ma

Publication date: 16 April 2008

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2005.11.002

zbMATH Keywords

mixingtransitivityweak mixingchaoticity

Mathematics Subject Classification ID

Topological dynamics (37B99) Dynamical systems involving maps of the interval (37E05)

Related Items (14)

Mixing properties of set-valued maps on hyperspaces via Furstenberg families ⋮ Iterated function systems and well-posedness ⋮ Characterizing ergodicity of induced hyperspace dynamical systems ⋮ \(\mathcal L\)-fuzzy Euclidean normed spaces and compactness ⋮ Scale-invariant occupancy of phase space and additivity of nonextensive entropy \(S_q\) ⋮ Chaos of Transformations Induced Onto the Space of Probability Measures ⋮ A note on stronger forms of sensitivity for dynamical systems ⋮ Some stronger forms of topological transitivity and sensitivity for a sequence of uniformly convergent continuous maps ⋮ F-sensitivity and (F_1, F_2)-sensitivity between dynamical systems and their induced hyperspace dynamical systems ⋮ Chaos in non-autonomous discrete systems and their induced set-valued systems ⋮ FURTHER DISCUSSION ON KATO'S CHAOS IN SET-VALUED DISCRETE SYSTEMS ⋮ Inducing sensitivity on hyperspaces ⋮ Sensitive dependence on initial conditions between dynamical systems and their induced hyperspace dynamical systems ⋮ Topological conjugacy between induced non-autonomous set-valued systems and subshifts of finite type

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamics in one dimension
• On maps with dense orbits and the definition of chaos
• A note on transitivity in set-valued discrete systems.
• Chaos of discrete dynamical systems in complete metric spaces
• On chaotic set-valued discrete dynamical systems
• Defining Chaos
• On Devaney's Definition of Chaos
• Period Three Implies Chaos
• Entropy and periodic points for transitive maps
• On Intervals, Transitivity = Choas
• Chaos, Periodicity, and Snakelike Continua

This page was built for publication: Individual chaos implies collective chaos for weakly mixing discrete dynamical systems