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arXiv · 2510.18804

Continuity of Lyapunov exponents for C^r one-dimensional maps

Alexandre Delplanque·Hengyi Li
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Abstract

We prove the entropic continuity of Lyapunov exponent for C^r maps of the interval or of the circle with large entropy for r>1, without making any assumptions on the set of critical points. A consequence is the upper semi-continuity of entropy at ergodic measures with large entropy. Another consequence is the uniform integrability of the geometric potential at ergodic measures with large entropy.

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Alexandre Delplanque, Hengyi Li. 2025-10-21. Continuity of Lyapunov exponents for C^r one-dimensional maps. https://arxiv.org/abs/2510.18804

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