The average shadowing property and chaos for continuous flows

DOI10.1080/1726037X.2017.1390190zbMath1499.37059OpenAlexW2771814019MaRDI QIDQ5069590

Yingxuan Niu

Publication date: 19 April 2022

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

Full work available at URL: https://doi.org/10.1080/1726037x.2017.1390190

zbMATH Keywords

almost periodic pointLyapunov stabletopological ergodicityAuslander-Yorke chaosaverage-shadowing property

Mathematics Subject Classification ID

Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems (37B65)

Related Items (3)

The equivalent condition of \(G\)-asymptotic tracking property and \(G\)-Lipschitz tracking property ⋮ The \(G\)-sequence shadowing property and \(G\)-equicontinuity of the inverse limit spaces under group action ⋮ Dynamical property of the shift map under group action

Cites Work

• The average-shadowing property and strong ergodicity
• A note on the average shadowing property for expansive maps
• Various shadowing properties for positively expansive maps
• The average-shadowing property and transitivity for continuous flows
• The average-shadowing property and topological ergodicity
• The average-shadowing property and topological ergodicity for flows
• Small perturbations of chaotic dynamical systems
• Topological chaos: what may this mean?
• Period Three Implies Chaos
• Strong ergodicity of systems with the average shadowing property
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Diffeomorphisms with the average-shadowing property on two-dimensional closed manifolds
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