A Hölder-Type Inequality for the C0 Distance and Anosov–Katok Pseudo-Rotations

Abstract

We prove a Hölder-type inequality for Hamiltonian diffeomorphisms relating the C⁰ norm, the C⁰ norm of the derivative, and the Hofer/spectral norm. We obtain as a consequence that sufficiently fast convergence in Hofer/spectral metric forces C⁰ 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 C⁰ rigidity result for such pseudo-rotations.