Full-dimensional KAM torus with frequency-preserving in infinite-dimensional Hamiltonian systems

Autor:	Tong, Zhicheng, Li, Yong
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems 37K55 35Q55
Druh dokumentu:	Working Paper
Popis:	In this paper, we present two infinite-dimensional KAM theorems with frequency-preserving for a nonresonant frequency of Diophantine type or even weaker. To be more precise, under a nondegenerate condition for an infinite-dimensional Hamiltonian system, we prove the persistence of a full-dimensional KAM torus with the specified frequency independent of any spectral asymptotics, by advantage of the generating function method. This appears to be the first Kolmogorov type result in the infinite-dimensional context. As a direct application, we provide a positive answer to Bourgain's conjecture: full-dimensional invariant tori for 1D nonlinear Schr\"{o}dinger equations do exist. Comment: We found that there seemed to be some problems with the validation of the hypothesis, and we are trying to fix them.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.01864 Zobrazit plný text záznamu View this record from Arxiv