Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves

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

2012-04-20

arxiv.org/abs/1204.4694v1

Mathematics

Dynamical Systems

36 pages, 2 figures

Scientific paper

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.

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