Orateur
Chengyang Shao
(IHES, Univ. Paris Saclay)
Description
In this talk, we aim to present an alternative formulation of classical KAM theory via paradifferential calculus. A powerful tool introduced by J.-M. Bony during the 80s, paradifferential calculus is widely used in delicate analysis of nonlinearities. Based on a tailored definition of paraproduct operators, it turns out that dynamical conjugacy problems involving "small denominators" can be transformed into fixed point forms. Compared to the well-known KAM iteration, this alternative scheme is numerically easier to manipulate with. Hopefully, this numerical scheme could contribute to “KAM theory with realistic parameters”. The talk is based on joint works with Thomas Alazard, Jacques Fejoz and Kuang Huang.
