G-Chain Mixing and G-Chain Transitivity in Metric G-Space - Zhanjiang Ji (Advances in Mathematical Physics)
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.