Analytic pseudo-rotations
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866918091798085632 |
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| author | Berger, Pierre |
| author_facet | Berger, Pierre |
| contents | We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points and which are not conjugated to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen ergodic or to the contrary with local emergence of maximal order. In particular, this disproves a conjecture of Birkhoff (1941) and solve a problem of Herman (1998). One aspect of the proof provides a new approximation theorem, it enables in particular to implement the Anosov-Katok scheme in new analytic settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_03438 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Analytic pseudo-rotations Berger, Pierre Dynamical Systems Symplectic Geometry We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points and which are not conjugated to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen ergodic or to the contrary with local emergence of maximal order. In particular, this disproves a conjecture of Birkhoff (1941) and solve a problem of Herman (1998). One aspect of the proof provides a new approximation theorem, it enables in particular to implement the Anosov-Katok scheme in new analytic settings. |
| title | Analytic pseudo-rotations |
| topic | Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2210.03438 |