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- Title
On the Eventual Shadowing Property and Eventually Shadowable Point of Set-valued Dynamical Systems.
- Authors
Xie, Xue Rong; Yin, Jian Dong
- Abstract
The authors introduce the concepts of the eventual shadowing property and eventually shadowable point for set-valued dynamical systems and prove that a set-valued dynamical system has the eventual shadowing property if and only if every point in the phase space is eventually shadowable; every chain transitive set-valued dynamical system has either the eventual shadowing property or no eventually shadowable points; and a set-valued dynamical system admits an eventually shadowable point if and only if it admits a minimal eventually shadowable point. Moreover, it is proved that a set-valued dynamical system with the eventual shadowing property is chain mixing if and only if it is mixing and if and only if it has the specification property.
- Subjects
DYNAMICAL systems; PHASE space
- Publication
Acta Mathematica Sinica, 2022, Vol 38, Issue 6, p1105
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-022-1041-6