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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.15303 |
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| _version_ | 1866911841633959936 |
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| author | Berger, Pierre |
| author_facet | Berger, Pierre |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15303 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic pseudo-rotations II: a principle for spheres, disks and annuli Berger, Pierre Dynamical Systems 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. |
| title | Analytic pseudo-rotations II: a principle for spheres, disks and annuli |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2402.15303 |