Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces

被引：9

作者：

Garcia, Isaac A. ^{[1
]}

Hernandez-Bermejo, Benito ^{[2
]}

机构：

[1] Univ Lleida, Dept Matemat, Lleida 25001, Spain

[2] Univ Rey Juan Carlos, Dept Fis, Madrid 28933, Spain

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2010年 / 239卷 / 17期

关键词：

Poisson systems; Casimir invariants; Hamiltonian systems; Perturbation theory; Limit cycles; Poincare-Pontryagin theory; POISSON STRUCTURES; GLOBAL ANALYSIS; SYSTEMS; CLASSIFICATION; EQUATIONS; FAMILY;

D O I：

10.1016/j.physd.2010.04.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Analytical perturbations of the Euler top are considered. The perturbations are based on the Poisson structure for such a dynamical system, in such a way that the Casimir invariants of the system remain invariant for the perturbed flow. By means of the Poincare-Pontryagin theory, the existence of limit cycles on the invariant Casimir surfaces for the perturbed system is investigated up to first order of perturbation, providing sharp bounds for their number. Examples are given. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1665 / 1669

页数：5

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