Entropy Continuity of Lyapunov Exponents for Non-flat 1-dimensional Maps

TL;DR

This paper extends the continuity of Lyapunov exponents from smooth surface diffeomorphisms to smooth interval maps with non-flat critical points, establishing uniform integrability over entropies.

Contribution

It proves the stronger property of entropy continuity for Lyapunov exponents in one-dimensional maps with non-flat critical points, generalizing previous results.

Findings

Lyapunov exponents are continuous for these maps.

Uniform integrability of Lyapunov exponents over entropy sequences.

Extension of continuity results from surface diffeomorphisms to interval maps.

Abstract

We show that the continuity property of Lyapunov exponents proved in \cite{BCS-Exponents} for smooth surface diffeomorphisms extends to smooth interval maps, in the case when the map only has non-flat critical points and the entropies converging to the topological entropy. The result we obtained is stronger than the continuity of Lyapunov exponents. In particular, we prove the uniform integrability of Lyapunov exponents over entropies.