Sensitivity and Devaney's chaos in uniform spaces

DOI10.1007/s10883-013-9182-7zbMath1338.37015arXiv1109.2029OpenAlexW2060661880MaRDI QIDQ372885

Michel Coornaert, Tullio G. Ceccherini Silberstein

Publication date: 21 October 2013

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.2029

Mathematics Subject Classification ID

Uniform structures and generalizations (54E15) Symbolic dynamics (37B10) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (38)

Rigidity and sensitivity on uniform spaces ⋮ Topological entropy, pseudo-orbits and uniform spaces ⋮ Specification property for topological spaces ⋮ What is topological about topological dynamics? ⋮ Specification properties on uniform spaces ⋮ Sensitivity, Devaney's chaos and Li-Yorke \(\varepsilon \)-chaos ⋮ Chaos and weak mixing on uniform spaces ⋮ Li-Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts ⋮ Topological entropy of nonautonomous dynamical systems on uniform spaces ⋮ Chaotic foliations with Ehresmann connection ⋮ Devaney's and Li-Yorke's chaos in uniform spaces ⋮ Equicontinuity, shadowing and distality in general topological spaces ⋮ On M-dynamics and Li-Yorke chaos of extensions of minimal dynamics ⋮ Sensitivity, property P and uniform entropy ⋮ Chaotic actions of topological semigroups ⋮ Unnamed Item ⋮ Chaos in Cartan foliations ⋮ Sofic boundaries of groups and coarse geometry of sofic approximations ⋮ A note on sensitivity in uniform spaces ⋮ Topological Ergodic Shadowing and Chaos on Uniform Spaces ⋮ Various types of shadowing and specification on uniform spaces ⋮ Equicontinuity, transitivity and sensitivity: the Auslander-Yorke dichotomy revisited ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Expansivity for measures on uniform spaces ⋮ Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics ⋮ Ultragraph shift spaces and chaos ⋮ Extended symmetry groups of multidimensional subshifts with hierarchical structure ⋮ Unnamed Item ⋮ A note on uniform entropy for maps having topological specification property ⋮ Stronger forms of sensitivity in the dynamical system of abelian semigroup actions ⋮ Chaos, attraction, and control for semigroup actions ⋮ Relationship among several types of sensitivity in general semi-flows ⋮ Orbital shadowing, \(\omega\)-limit sets and minimality ⋮ Sensitivity of Nonautonomous Dynamical Systems on Uniform Spaces ⋮ Some dynamical properties of syndetic subsemigroups actions ⋮ Topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces ⋮ Transitivity and sensitivity of semigroup actions on uniform spaces

Cites Work

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• The Myhill property for strongly irreducible subshifts over amenable groups
• On maps with dense orbits and the definition of chaos
• A note on sensitivity of semigroup actions
• On the density of periodic configurations in strongly irreducible subshifts
• Cellular Automata and Groups
• On Devaney's Definition of Chaos
• Sensitive dependence on initial conditions

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