Federico Rodriguez-Hetrz

Exponential volume limits

Let $M$ be a $d$-dimensional closed Riemannian manifold, let $f\in\mathrm{Diff}^{1+β}(M)$, and denote by $m$ the Riemannian volume form of $M$. We prove that if $m\circ f^{-n}\xrightarrow[n\to\infty]{}μ$ exponentially fast, then $μ$ is an SRB measure.