Embedding asymptotically expansive systems

作者：Burguet David^*

来源：Monatshefte fur Mathematik, 2017, 184(1): 21-49.

DOI：10.1007/s00605-017-1079-1

• Entropy
• Expansiveness
• Generators

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 #Per(n) (X,T) <= 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.

• 出版日期2017-9