Uniformly Positive Entropy of Induced Transformations

Abstract

Let $(X,T)$ be a topological dynamical system consisting of a compact metric space $X$ and a continuous surjective map $T:X\to X$. By using local entropy theory, we prove that $(X,T)$ has uniformly positive entropy if and only if so does the induced system $(\cM(X),\wt{T})$ on the space of Borel probability measures endowed with the weak${}^{\ast }$ topology. This result can be seen as a version for the notion of uniformly positive entropy of the corresponding result for topological entropy due to Glasner and Weiss.

To apper in ETDS

References in corpus (3)

• Graph Theoretic Structure of Maps of the Cantor Space
• On the Dynamics of Induced Maps on the Space of Probability Measures
• Dynamics of Induced Systems