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

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.

💡 Research Summary

The paper investigates the relationship between entropy convergence and Lyapunov exponent continuity for smooth one‑dimensional interval maps that possess only non‑flat critical points. The setting is a C^∞ map f on either the unit interval