This article is cited in 1 paper

Special Issue: 70 Years of KAM Theory (Issue Editors: Alessandra Celletti, Luigi Chierchia, and Dmitry Treschev)

On Elliptic Lower-Dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems with Small Parameters

Hanru Zou, Junxiang Xu

School of Mathematics, Southeast University, 210096 Nanjing, China

Abstract: In this paper we consider the persistence of elliptic lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems with small parameters. Under the Brjuno nondegeneracy condition, if the prescribed frequencies satisfy a Diophantine condition, by the KAM technique we prove that for most of small parameters in the sense of Lebesgue measure, the Hamiltonian systems admit a lower-dimensional invariant torus whose frequency vector is a dilation of the prescribed frequencies.

Keywords: Hamiltonian system, invariant tori, KAM iteration, Brjuno nondegeneracy condition

MSC: 37J40, 37J25, 37J05

Received: 28.06.2023
Accepted: 03.06.2024

Language: English

DOI: 10.1134/S156035472404004X