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

par Dusan Joksimovic (IMJ-PRG)

vendredi 21 oct. 2022, 10:30 → 11:30 Europe/Paris

112 (ICJ)

In this talk, we will show that sufficiently fast convergence in Hofer/spectral metric forces $C^0$^{^^}  convergence. We achieve this by proving a Hölder-type inequality for Hamiltonian diffeomorphisms relating the $C^0$ norm, the $C^0$ norm of the derivative, and the Hofer/spectral norm. As an application of our Hölder-type inequality, we prove $C^0$^{^^} rigidity for a certain class of pseudo-rotations. 
In the first part of the talk, we will state the main results and prove the inequality. In the second part, we will introduce the class of Anosov-Katok pseudo-rotations, show how one can define their rotation number, and prove (using the inequality) that such pseudo-rotations with exponentially Liouville rotation numbers are $C^0$ rigid. This talk is based on joint work with Sobhan Seyfaddini.