  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.
