Entropy Continuity of Lyapunov Exponents for Non-flat 1-dimensional Maps
Dynamical Systems
2026-03-13 v2
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.
Keywords
Cite
@article{arxiv.2412.19007,
title = {Entropy Continuity of Lyapunov Exponents for Non-flat 1-dimensional Maps},
author = {Hengyi Li},
journal= {arXiv preprint arXiv:2412.19007},
year = {2026}
}