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

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.

arXiv comment40 pages, comments are welcome