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CONTINUOUS SHADOWING AND STABILITY FOR GROUP ACTIONS

Kim, Sang Jin

  • Received : 2018.01.17
  • Accepted : 2018.10.12
  • Published : 2019.01.01

Abstract

Recently, Chung and Lee [2] introduced the notion of topological stability for a finitely generated group action, and proved a group action version of the Walters's stability theorem. In this paper, we introduce the concepts of continuous shadowing and continuous inverse shadowing of a finitely generated group action on a compact metric space X with respect to various classes of admissible pseudo orbits and study the relationships between topological stability and continuous shadowing and continuous inverse shadowing property of group actions. Moreover, we introduce the notion of structural stability for a finitely generated group action, and we prove that an expansive action on a compact manifold is structurally stable if and only if it is continuous inverse shadowing.

Keywords

continuous shadowing;expansiveness;group action;inverse shadowing;structural stability;topological stability

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)