2020
DOI: 10.3934/dcdsb.2019231
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Ergodicity of non-autonomous discrete systems with non-uniform expansion

Abstract: We study the ergodicity of non-autonomous discrete dynamical systems with nonuniform expansion. As an application we get that any uniformly expanding finitely generated semigroup action of C 1+α local diffeomorphisms of a compact manifold is ergodic with respect to the Lebesgue measure. Moreover, we will also prove that every exact non-uniform expandable finitely generated semigroup action of conformal C 1+α local diffeomorphisms of a compact manifold is Lebesgue ergodic.

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Cited by 1 publication
(2 citation statements)
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“…i) We say that IFS(X; F) is weak topologically exact if for every open set U , there exists a finite sequence [10]We say that IFS(X; F) is topologically exact if for every open set U , there exists a sequence (T i ) i∈N in F + so that i T i (U ) = X.…”
Section: Dynamical Systems Of Relationsmentioning
confidence: 99%
See 1 more Smart Citation
“…i) We say that IFS(X; F) is weak topologically exact if for every open set U , there exists a finite sequence [10]We say that IFS(X; F) is topologically exact if for every open set U , there exists a sequence (T i ) i∈N in F + so that i T i (U ) = X.…”
Section: Dynamical Systems Of Relationsmentioning
confidence: 99%
“…ii) [10]We say that IFS(X; F) is topologically exact if for every open set U , there exists a sequence…”
Section: Dynamical Systems Of Relationsmentioning
confidence: 99%