A note on the average shadowing property for expansive maps

DOI10.1016/j.topol.2011.04.016zbMath1237.37018OpenAlexW2049128222MaRDI QIDQ649787

Dominik Kwietniak, Piotr Oprocha

Publication date: 6 December 2011

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2011.04.016

zbMATH Keywords

transitivityaverage shadowing propertyweak mixingshadowingexpansive map

Mathematics Subject Classification ID

Related Items (29)

Dynamics of induced maps on the space of probability measures ⋮ The specification property and infinite entropy for certain classes of linear operators ⋮ The average shadowing property and chaos for continuous flows ⋮ Entropy of irregular points for some dynamical systems ⋮ Relations of the almost average shadowing property with ergodicity and proximality ⋮ The \(G\)-sequence shadowing property and \(G\)-equicontinuity of the inverse limit spaces under group action ⋮ Unnamed Item ⋮ Some dynamical properties for free semigroup actions ⋮ Generalized specification property and distributionally scrambled sets ⋮ Some properties of dynamical systems having shadowing ⋮ Average shadowing and gluing property ⋮ Unnamed Item ⋮ Operators with the specification property ⋮ Devaney chaos plus shadowing implies distributional chaos ⋮ Unnamed Item ⋮ On controlled specification and uniqueness of the equilibrium state in expansive systems ⋮ Shadowing, Entropy and Minimal Sets ⋮ Suspensions of homeomorphisms with the two-sided limit shadowing property ⋮ Controlled shadowing property ⋮ Various types of shadowing and specification on uniform spaces ⋮ Strong ergodicity of systems with the average shadowing property ⋮ Average shadowing and persistence in pointwise dynamics ⋮ On partial shadowing of complete pseudo-orbits ⋮ Measure expansivity and specification for pointwise dynamics ⋮ The \(G\)-asymptotic tracking property and \(G\)-asymptotic average tracking property in the inverse limit spaces under group action ⋮ Average Shadowing Property and Asymptotic Average Shadowing Property of Linear Dynamical Systems ⋮ Geodesic Flows Modelled by Expansive Flows ⋮ Chain mixing, shadowing properties and multi-transitivity ⋮ Unnamed Item

Cites Work

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• The average-shadowing property and strong ergodicity
• Ergodic theory on compact spaces
• Various shadowing properties for positively expansive maps
• Weak mixing and product recurrence
• Chain recurrence rates and topological entropy
• Deterministic Properties of Stochastically Perturbed Dynamic Systems
• Spectral Decomposition Theorem for non-hyperbolic maps
• Metric properties of ε-trajectories of dynamical systems with stochastic behaviour
• Dynamical systems disjoint from any minimal system
• Periodic Points and Measures for Axiom a Diffeomorphisms

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