Weighted Topological Entropy of the Set of Generic Points in Topological Dynamical Systems

摘要

This article is devoted to the investigation of the weighted topological entropy of generic points of the ergodic measures in dynamical systems. We showed that the weighted topological entropy of generic points of the ergodic measure is equal to the weighted measure entropy of which generalized the classical result of Bowen (Trans Am Math Soc 184:125-136, 1973). As an application, we also use the result to study the dimension of generic points for a class of skew product expanding maps on high dimensional tori.