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arXiv · 2402.15303

Analytic pseudo-rotations II: a principle for spheres, disks and annuli

Pierre Berger
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Abstract

We construct analytic surface symplectomorphisms with unstable elliptic fixed points; this solves a problem of Birkhoff (1927). More precisely, we construct analytic symplectomorphisms of the sphere and of the disk which are transitive, with respectively only 2 and 1 periodic points. This also solves problems of proposed by Herman (1998), Fayad-Katok (2004) and Fayad-Krikorian (2018). To establish these results, we introduce a principle that enables to realize, by an analytic symplectomorphism, properties which are $C^0$-realizable by the approximation by conjugacy method of Anosov-Katok.

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Pierre Berger. 2024-02-23. Analytic pseudo-rotations II: a principle for spheres, disks and annuli. https://arxiv.org/abs/2402.15303

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