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G-Chain Mixing and G-Chain Transitivity in Metric G-Space

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  • Zhanjiang Ji
  • Mohammad Mirzazadeh

Abstract

Firstly, we introduce the concept of G-chain mixing, G-mixing, and G-chain transitivity in metric G-space. Secondly, we study their dynamical properties and obtain the following results. (1) If the map f has the G-shadowing property, then the map f is G-chain mixed if and only if the map f is G-mixed. (2) The map f is G-chain transitive if and only if for any positive integer k≥2, the map fk is G-chain transitive. (3) If the map f is G-pointwise chain recurrent, then the map f is G-chain transitive. (4) If there exists a nonempty open set U satisfying GU=U, U¯≠X, and fU¯⊂U, then we have that the map f is not G-chain transitive. These conclusions enrich the theory of G-chain mixing, G-mixing, and G-chain transitivity in metric G-space.

Suggested Citation

  • Zhanjiang Ji & Mohammad Mirzazadeh, 2022. "G-Chain Mixing and G-Chain Transitivity in Metric G-Space," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-7, January.
    • Handle: RePEc:hin:jnlamp:1109686
    DOI: 10.1155/2022/1109686
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