Raphael Krikorian: On local integrability of real analytic conservative diffeomorphisms in dimension 2

Date: 2023-03-02

Time: 15:00 - 16:00


Raphael Krikorian, The University of Cergy-Pontoise


Let TWIP be the class of smooth   diffeomorphisms of the 2-disk or the 2-cylinder that  admit  a non resonant/Diophantine elliptic equilibrium, have the intersection property and satisfy a twist condition. Birkhoff Normal Form and KAM theory tell us that this elliptic equilibrium is accumulated by a positive measure set of invariant  KAM circles. I shall present in this talk a proof of the following result: any   real analytic TWIP diffeomorphism is accumulated in the real analytic topology by real analytic TWIP’s that  are locally integrable at the origin, which means that an neighborhood  of the origin (depending on the order of approximation) is fully covered by KAM invariant circles. The proof is based on KAM theory and  arguments from sheaf theory and   deformation of complex structures.