Séminaire Jeunes chercheurs (Pierre Schatz, jeudi 24 octobre 2024)

La prochaine séance du séminaire Jeunes chercheurs du CEREMADE aura lieu le jeudi 24 octobre 2024 à 17h en salle A707. Nous aurons le plaisir d'écouter Pierre Schatz (Ecole polytechnique), qui nous parlera de

Ridigity in elliptic dynamics

Abstract
In this presentation, we will give an historic of rigidity results in elliptic dynamics, followed by a link to more recent questions, and how it can help to answer some conjectures in hamiltonian dynamics. We will begin by defining what is a dynamical system, give some context about the questions often asked in this domain, then switch to elliptic dynamics (basically, elliptic opposes itself to hyperbolicity : the first is the world of rotations, of "no deformations", and the second is the world of contractions and dilatations). We will then discuss about linearisation results for holomorphic diffeomorphisms, studied by Poincaré and "solved" by Siegel and Yoccoz. At the very end, we will give a glance to a similar result in hamiltonian dynamics, that we have proved in dimension 1.