2 papers
math.DS2025
Continuity of Lyapunov exponents for C^r one-dimensional maps
Alexandre Delplanque, Hengyi Li
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 critica…
math.DS2024
Hyperbolic absolutely continuous invariant measures for C^r one-dimensional maps
Alexandre Delplanque
For r > 1, we show, using the Ledrappier-Young entropy characterization of SRB measures for non-invertible maps, that if a C^r map f of the interval or the circle has its Lyapunov…