# Problem 133

## Primary tabs

$C^ \infty$ diffeo of the 2-disk preserving a smooth measure $\mu$ with $h_\mu >0$? An ergodic example?

## Tags

### BHM

He also asks about entropy of Hamiltonian system in Arnold-Avez

### See Katok, A. Bernoulli

See Katok, A. Bernoulli diffeomorphisms on surfaces. Ann. of Math. (2) 110 (1979), no. 3, 529--547.

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