Conférence de systèmes dynamiques.
Résumé
The classical Birkhoff conjecture states that the only integrable convex planar domains are circles and ellipses. We show that this conjecture is true for perturbations of ellipses. It turns out that the method of proof gives an insight into deformational spectral rigidity of planar axis symmetric domains and gives a partial answer to a question of P. Sarnak.
This is based on several papers with Avila, De Simoi, G. Huang, Sorrentino, and Q. Wei.
