The sharp $C^0$-fragmentation property for Hamiltonian diffeomorphisms and homeomorphisms on surfaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908589925335040 |
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| author | Serraille, Baptiste |
| author_facet | Serraille, Baptiste |
| contents | In this paper, we present a $C^0$-fragmentation property for Hamiltonian diffeomorphisms. More precisely, it is known that for a given open covering $\mathcal{U}$ of a compact symplectic surface we can write each $C^0$-small enough Hamiltonian diffeomorphism as the composition of Hamiltonian diffeomorphisms compactly supported inside the open sets of the covering $\mathcal{U}$. We show that such a decomposition can be done with a Lipschitz estimate on the $C^0$-norm of the fragments. We also show the same property for the kernel of $θ$, the mass-flow homomorphism for homeomorphisms. This answers a question from Buhovsky and Seyfaddini. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The sharp $C^0$-fragmentation property for Hamiltonian diffeomorphisms and homeomorphisms on surfaces Serraille, Baptiste Symplectic Geometry Differential Geometry 57S05, 53D99, 54C20, 51M25 In this paper, we present a $C^0$-fragmentation property for Hamiltonian diffeomorphisms. More precisely, it is known that for a given open covering $\mathcal{U}$ of a compact symplectic surface we can write each $C^0$-small enough Hamiltonian diffeomorphism as the composition of Hamiltonian diffeomorphisms compactly supported inside the open sets of the covering $\mathcal{U}$. We show that such a decomposition can be done with a Lipschitz estimate on the $C^0$-norm of the fragments. We also show the same property for the kernel of $θ$, the mass-flow homomorphism for homeomorphisms. This answers a question from Buhovsky and Seyfaddini. |
| title | The sharp $C^0$-fragmentation property for Hamiltonian diffeomorphisms and homeomorphisms on surfaces |
| topic | Symplectic Geometry Differential Geometry 57S05, 53D99, 54C20, 51M25 |
| url | https://arxiv.org/abs/2403.15767 |