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arXiv · 2403.15767

The sharp $C^0$-fragmentation property for Hamiltonian diffeomorphisms and homeomorphisms on surfaces

Baptiste Serraille
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Abstract

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 $\theta$, the mass-flow homomorphism for homeomorphisms. This answers a question from Buhovsky and Seyfaddini.

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Baptiste Serraille. 2024-03-23. The sharp $C^0$-fragmentation property for Hamiltonian diffeomorphisms and homeomorphisms on surfaces. https://arxiv.org/abs/2403.15767

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