Equivalent characterizations of hyperbolic H\"older potential for interval maps

TL;DR

This paper provides two equivalent ways to characterize hyperbolic Hölder potentials for certain interval maps, linking Lyapunov exponents and measure-theoretic entropies of equilibrium states.

Contribution

It introduces new equivalent characterizations of hyperbolic Hölder potentials for topologically exact $C^3$ interval maps without non-flat critical points.

Findings

Two equivalent characterizations in terms of Lyapunov exponents and entropies.

Applicable to topologically exact $C^3$ interval maps.

Builds on previous work to deepen understanding of hyperbolic potentials.

Abstract

Consider a topologically exact $C^3$ interval map without non-flat critical points. Following the works we did in \cite{LiRiv12two}, we give two equivalent characterizations of hyperbolic H\"{o}lder continuous potential in terms of the Lyapunov exponents and the measure-theoretic entropies of equilibrium states for those potentials.