Density-Equicontinuity and Density-Sensitivity of Discrete Amenable Group Actions.

Autor:	Liu, Xiusheng, Yin, Jiandong
Předmět:	METRIC spaces TOPOLOGICAL entropy INVARIANT measures ABELIAN groups GROUP actions (Mathematics) COMPACT spaces (Topology)
Zdroj:	Journal of Dynamics & Differential Equations; Jun2024, Vol. 36 Issue 2, p1851-1872, 22p
Abstrakt:	Let (X, G) be a G-system which means that X is a compact metric space and G is an amenable group continuously acting on X. In this paper, we introduce the notions of density-equicontinuity with respect to a given Følner sequence and Banach density-equicontinuity for amenable group actions and we give some relations among Banach mean equicontinuity, Banach density-t-equicontinuity and Banach density-equicontinuity. Moreover, we introduce the concept of density n-sensitive tuple with respect to a given Følner sequence for amenable group actions and we prove that every topological sequence entropy n-tuple is a density n-sensitive tuple with respect to each tempered Følner sequence for an abelian group action which admits an ergodic measure with full support. For an invariant measure μ of (X, G), we introduce the concept of μ -density n-sensitive tuple with respect to a given Følner sequence and we show that if μ is ergodic and G is abelian, then every μ -sequence entropy n-tuple is a μ -density n-sensitive tuple with respect to any given tempered Følner sequence of G. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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