Numerical Computation of Critical Surfaces for the Breakup of Invariant Tori in Hamiltonian Systems

被引：0

作者：

Bustamante, Adrian P. ^{[1
]}

Chandre, Cristel ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Aix Marseille Univ, CNRS, I2M, F-13009 Marseille, France

来源：

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2023年 / 22卷 / 01期

基金：

欧盟地平线“2020”;

关键词：

Hamiltonian systems; KAM; invariant tori; renormalization; RENORMALIZATION-GROUP; KAM THEORY; UNIVERSALITY;

D O I：

10.1137/21M1448501

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We compute the critical surface for the existence of invariant tori of a family of Hamiltonian systems with two and three degrees of freedom. We use and compare two methods to compute the critical surfaces: renormalization-group transformations and conjugation in configuration space. We unveil the presence of cusps in the critical surface for the breakup of three-dimensional invariant tori of Hamiltonian systems with three degrees of freedom, whereas the critical surface of two-dimensional invariant tori of Hamiltonian systems with two degrees of freedom is expected to be smooth.

引用

页码：483 / 500

页数：18

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