Normal forms near two-dimensional resonance tori for the multidimensional anharmonic oscillator

被引：1

作者：

Dobrokhotov, SY ^{[1
]}

Poteryakhin, MA ^{[1
]}

机构：

[1] Russian Acad Sci, Inst Problems Mech, Moscow 117901, Russia

来源：

MATHEMATICAL NOTES | 2004年 / 76卷 / 5-6期

关键词：

normal form; isotropic torus; resonance torus; anharmonic oscillator; invariant manifold; Hamiltonian system;

D O I：

10.1023/B:MATN.0000049664.77226.52

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the problem of constructing a normal form near a two-dimensional invariant isotropic torus for a multidimensional anharmonic oscillator. We construct a fourth-order normal form with respect to harmonic oscillator type variables. We show that, in the presence of resonances, the dependence of the normal form on the action type variables become,nonpolynomial.

引用

页码：653 / 664

页数：12

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