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Pré-Publication, Document De Travail Année : 2022

A H\"older-type inequality for the $C^0$ distance and Anosov-Katok pseudo-rotations

Résumé

We prove a H\"older-type inequality for Hamiltonian diffeomorphisms relating the $C^0$ norm, the $C^0$ norm of the derivative, and the Hofer/spectral norm. We obtain as a consequence that sufficiently fast convergence in Hofer/spectral metric forces $C^0$ convergence. The second theme of our paper is the study of pseudo-rotations that arise from the Anosov-Katok method. As an application of our H\"older-type inequality, we prove a $C^0$ rigidity result for such pseudo-rotations.

Dates et versions

hal-03860907 , version 1 (18-11-2022)

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Dušan Joksimović, Sobhan Seyfaddini. A H\"older-type inequality for the $C^0$ distance and Anosov-Katok pseudo-rotations. 2022. ⟨hal-03860907⟩
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