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

Zhanjiang Ji

Advances in Mathematical Physics, 2022, vol. 2022, issue 1

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 G(U) = 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.

Date: 2022
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https://doi.org/10.1155/2022/1109686

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:1109686

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