Continuity of Lyapunov exponents for Cr one-dimensional maps
Abstract
We prove the entropic continuity of Lyapunov exponent for Cr 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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