Regularity of absolutely continuous invariant measures for piecewise expanding unimodal maps

Fabian Contreras, Dmitry Dolgopyat

Let $f:[0,1]\to [0,1]$ be a piecewise expanding unimodal map of class $C^{k+1}$, with $k\ge 1$, and $\mu =\rho dx$ the (unique) SRB measure associated to it. We study the regulari…