On the shadowing property and shadowable point of set-valued dynamical systems

DOI10.1007/s10114-020-9331-3zbMath1461.37024OpenAlexW3113742950MaRDI QIDQ1995605

Xiao Fang Luo, Xiao Xiao Nie, Jian Dong Yin

Publication date: 24 February 2021

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-020-9331-3

zbMATH Keywords

shadowing propertyspecificationset-valued dynamical systemshadowable point

Mathematics Subject Classification ID

Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems (37B65)

Related Items (5)

The equivalent condition of \(G\)-asymptotic tracking property and \(G\)-Lipschitz tracking property ⋮ On the eventual shadowing property and eventually shadowable point of set-valued dynamical systems ⋮ The \(G\)-sequence shadowing property and \(G\)-equicontinuity of the inverse limit spaces under group action ⋮ Unnamed Item ⋮ Metric entropy for set-valued maps

Cites Work

• Minimal invariant closed sets of set-valued semiflows
• Shadowable points for flows
• Shadowing with chain transitivity
• Properties of shadowable points: chaos and equicontinuity
• Multiple recurrence theorems for set-valued maps
• Shadowing property, weak mixing and regular recurrence
• Continuum-wise expansiveness and specification for set-valued functions and topological entropy
• Shadowable points
• Invariant Measures for Set-Valued Dynamical Systems
• Quantitative shadowable points
• The specification property on a set-valued map and its inverse limit
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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