Embedding asymptotically expansive system

Abstract

We prove a Krieger like embedding theorem for asymptotically expansive systems with the small boundary property. We show that such a system $(X;T)$ embeds in the $K$-full shift with $h_{top}(T)<\log K$ and $♯Pe{r}_n(X;T)\le ♯Pe{r}_n(\{1,...,K{\}}^{\mathbb{Z}};\sigma )$ for any integer $n$. The embedding is in general not continuous (unless the system is expansive and $X$ is zero-dimensional) but the induced map on the set of invariant measures is a topological embedding. It is shown that this property implies asymptotical expansiveness. We prove also that the inverse of the embedding map may be continuously extended to a faithful principal symbolic extension.

References in corpus (2)

• Embedding minimal dynamical systems into Hilbert cubes
• Prevalence of non-uniform hyperbolicity at the first bifurcation of Hénon-like families