In this article,we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological entropy and several equivalent conditions for the dynamical systems wit...In this article,we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological entropy and several equivalent conditions for the dynamical systems with the eventual shadowing property to be mixing.展开更多
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 i...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.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12061043)。
文摘In this article,we provide some sufficient conditions for the dynamical systems with the eventual shadowing property to have positive topological entropy and several equivalent conditions for the dynamical systems with the eventual shadowing property to be mixing.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12061043,11661054,11261039)。
文摘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.
