Geodesic
Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves
Barney Bramham1
1 Ruhr-Universität Bochum, Bochum, Germany
Annals of mathematics, Tome 181 (2015) no. 3, pp. 1033-1086.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2015.181.3.4

Barney Bramham 1

1 Ruhr-Universität Bochum, Bochum, Germany 
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Barney Bramham. Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves. Annals of mathematics, Tome 181 (2015) no. 3, pp. 1033-1086. doi : 10.4007/annals.2015.181.3.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.181.3.4/

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