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.

Sensitivity of iterated function systems

“…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.…”

“…ii) [10]We say that IFS(X; F) is topologically exact if for every open set U , there exists a sequence…”