IMJ-PRG Summer School 2024 - Stability and rigidity in dynamical systems, beyond classical KAM theory

Since Kolmogorov-Arnol’d-Moser’s theorem on stability of invariant tori in hamiltonian systems, the study of perturbations of systems with simple dynamics has been the object of intense research. The KAM method, based on an inductive scheme of successive conjugations, was applied in numerous settings to prove stability and rigidity results in dynamics. The main objective of the school is to give a panorama of the most important results and applications of the classical KAM theory as well as of the new directions of research in various areas of dynamics that pushed the theory way beyond its classical limits. This summer school will consist of 6 mini-courses of 5 hours each, accessible to PhD students and young researchers, as well as presentations of recent results in the domain. Mini-courses: - Modern developments of classical KAM theory (Luigi Chierchia, Univ. Roma 3) -Hamiltonian PDEs and KAM in infinite dimension (Michela Procesi, Univ. Roma 3) -Quasi-periodic Schrödinger operators (Raphaël Krikorian, Ecole Polytechnique) -Rigidity of higher rank algebraic actions (Danijela Damjanovic, KTH Stockholm, and Bassam Fayad, Univ. Maryland) -Coexistence between KAM and chaos (Abed Bounemoura, CNRS, CEREMADE) -Liouvillean constructions and inverse KAM theory (Masha Saprykina, KTH Stockholm)