A Hölder-type inequality for the $C^0$ distance and Anosov-Katok pseudo-rotations

Abstract

We prove a Hölder-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 Hölder-type inequality, we prove a $C^0$ rigidity result for such pseudo-rotations.

15 pages, the final version (contains minor changes compared to v2)

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