A volume preserving nonuniformly hyperbolic diffeomorphism with arbitrary number of ergodic components and close to the identity

Jianyu Chen, Huyi Hu, Yun Yang

We prove that for any $\ell\in\NN\cup\{\infty\}$ and any $r\in \NN$, every compact smooth Riemannian manifold $\cM$ of $\dim \cM\ge 5$ carries a $C^{\infty }$ volume preserving nonuni…