A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912280934875136 |
|---|---|
| author | Buhovsky, Lev Feuerstein, Ben Polterovich, Leonid Shelukhin, Egor |
| author_facet | Buhovsky, Lev Feuerstein, Ben Polterovich, Leonid Shelukhin, Egor |
| contents | We prove that autonomous Hamiltonian flows on the two-sphere exhibit the following dichotomy: the Hofer norm either grows linearly or is bounded in time by a universal constant C. Our approach involves a new technique, Hamiltonian symmetrization. Essentially, we prove that every autonomous Hamiltonian diffeomorphism is conjugate to an element C-close in the Hofer metric to one generated by a function of the height. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization Buhovsky, Lev Feuerstein, Ben Polterovich, Leonid Shelukhin, Egor Symplectic Geometry Dynamical Systems 53Dxx (Primary) 58D05, 22E65 (Secondary) We prove that autonomous Hamiltonian flows on the two-sphere exhibit the following dichotomy: the Hofer norm either grows linearly or is bounded in time by a universal constant C. Our approach involves a new technique, Hamiltonian symmetrization. Essentially, we prove that every autonomous Hamiltonian diffeomorphism is conjugate to an element C-close in the Hofer metric to one generated by a function of the height. |
| title | A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization |
| topic | Symplectic Geometry Dynamical Systems 53Dxx (Primary) 58D05, 22E65 (Secondary) |
| url | https://arxiv.org/abs/2408.08854 |