KAM via standard fixed point theorems

Orateur: Chengyang Shao
Localisation: Université de Chicago, États-Unis
Type: Groupe de travail équations aux dérivées partielles
Site: UPEC
Salle: P2-131
Date de début: 29/02/2024 - 13:45
Date de fin: 29/02/2024 - 14:45

 In this talk, we aim to introduce a new method to solve conjugacy problems involving 'small denominators’. Traditional proofs addressing the regularity loss caused by these 'small denominators' have heavily relied on Newtonian / Nash-Moser iterations. We aim to show that the regularity loss can be compensated by composing with appropriate para-differential operators, enabling a proof using only standard fixed-point schemes. This para-differential approach can be applied to study KAM-type problems, avoiding the commonly used 'KAM iterations.' The talk is based on joint works with Thomas Alazard.