On the dynamics and entropy of the push-forward map

TL;DR

This paper investigates the dynamical behavior and entropy characteristics of the push-forward map induced by a transformation T on probability measures, linking its topological entropy to that of T.

Contribution

It provides a detailed analysis of the push-forward map's dynamics and establishes a connection between its topological entropy and that of the original map T.

Findings

Established a relationship between topological entropies of T and the push-forward map

Analyzed the main dynamical properties of the push-forward map

Provided insights into the entropy dynamics in the space of probability measures

Abstract

In this work we study the main dynamical properties of the push-forward map, a transformation in the space of probabilities P(X) induced by a map T: X \to X, X a compact metric space. We also establish a connection between topological entropies of T and of the push-forward map.