Existence of SRB measures for expanding maps with weak regularity (Q2718007)

This paper is devoted to weak regularity on \(|\det Df(x)|\) such that a \(C^1\) (uniform) expanding map \(f\) does admit a unique absolutely continuous invariant probability measure \(\mu_0\) with respect to the Lebesgue measure \(m\). The authors show that any \(C^{1+\text{Dini}}\) expanding map \(f\) on any compact manifold admits a unique absolutely continuous invariant probability measure \(\mu_0\). Moreover the system \((f,\mu_0)\) is exact and therefore ergodic. NEWLINENEWLINENEWLINEThis generalizes related results of \textit{P. Gora} [Ergodic Theory Dyn. Syst. 14, 475-492 (1994; Zbl 0822.28008)] and \textit{K. Krzyzewski} and \textit{W. Szlenk} [Stud. Math. 33, 83-92 (1969; Zbl 0176.00901)].