## Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves

Barney Bramham

#### Abstract

We prove that every C^infty-smooth, area preserving diffeomorphism of the closed 2-disk having not more than one periodic point is the uniform limit of periodic C^infty-smooth diffeomorphisms. In particular every smooth irrational pseudo-rotation can be C^0-approximated by integrable systems. This partially answers a long standing question of A. Katok regarding zero entropy Hamiltonian systems in low dimensions. Our approach uses pseudoholomorphic curve techniques from symplectic geometry.

arXiv [DS] 1204.4694.