The local Hoelder exponent for the entropy of real unimodal maps

TL;DR

This paper demonstrates that the topological entropy of real unimodal maps varies in a Hoelder continuous manner with respect to the kneading parameter, and characterizes the local Hoelder exponent in terms of this function.

Contribution

It establishes the Hoelder continuity of topological entropy for unimodal maps and relates the local Hoelder exponent to the entropy function.

Findings

Topological entropy depends Hoelder continuously on the kneading parameter.

The local Hoelder exponent is proportional to the entropy function value.

Provides a mathematical characterization of entropy variation in unimodal maps.

Abstract

We prove that the topological entropy of real unimodal maps depends as a Hoelder continuous function of the kneading parameter, and the local Hoelder exponent equals, up to a factor log 2, the value of the function at that point.