Mutual Entropy Map for Continuous Systems on Compact Metric Spaces

In this paper we introduce the concept of mutual entropy map for continuous maps on metric spaces. It is a non-negative extended real number which depends on two measures which are preserved by a system. Then we will extract the Kolmogorov entropy of ergodic systems from the mutual entropy as a special case when the two measures are equal.

Keywords:

Entropy , Invariant , Mutual entropy.