A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems

被引：0

作者：

Caracciolo, Chiara ^{[1
,2
]}

Figueras, Jordi-Lluis ^{[1
]}

Haro, Alex ^{[3
]}

机构：

[1] Uppsala Univ, Dept Math, Uppsala, Sweden

[2] Univ Padua, Dept Math, Padua, Italy

[3] Univ Barcelona & Centrede Recerca Matemat, Dept Matemat & Informat, Barcelona, Spain

来源：

NONLINEARITY | 2025年 / 38卷 / 02期

基金：

瑞典研究理事会;

关键词：

lower dimensional invariant tori; KAM theory; parametrization method; QUASI-PERIODIC MAPS; INVARIANT TORI; PARAMETERIZATION METHOD; NORMAL-FORM; KAM THEORY; WHISKERS; THEOREM;

D O I：

10.1088/1361-6544/ada47b

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an algorithm for the construction of lower dimensional elliptic tori in parametric Hamiltonian systems by means of the parametrization method with the tangent and normal frequencies being prescribed. This requires that the Hamiltonian system has as many parameters as the dimension of the normal dynamics, and the algorithm must adjust these parameters. We illustrate the methodology with an implementation of the algorithm computing 2-dimensional elliptic tori in a system of 4 coupled anharmonic oscillators (4 degrees of freedom).

引用

页数：25

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