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arXiv · 1204.4694

Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves

Barney Bramham
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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.

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Barney Bramham. 2012-04-20. Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves. https://arxiv.org/abs/1204.4694

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