Embedding asymptotically expansive systems |
| |
Authors: | Email author" target="_blank">David?BurguetEmail author |
| |
Institution: | 1.LPMA - CNRS UMR 7599,Universite Paris 6,Paris Cedex 05,France |
| |
Abstract: | A topological dynamical system is said asymptotically expansive when entropy and periodic points grow subexponentially at arbitrarily small scales. 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 if \( h_{top}(T)<\log K\) and \(\sharp Per_n(X,T)\le K^n\) 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|