TOPOLOGY AND PERIODIC ORBITS OF RING-SHAPED POTENTIALS AS A GENERALIZED 4-D ISOTROPIC OSCILLATOR

被引：0

作者：

Balsas, M. C. ^{[1
]}

Ferrer, S. ^{[2
]}

Jimenez, E. S. ^{[1
]}

Vera, J. A. ^{[3
]}

机构：

[1] Univ Politecn Cartagena Murcia, Murcia, Spain

[2] Univ Murcia, E-30001 Murcia, Spain

[3] Ctr Univ Def MDE UPCT, Murcia 30720, Spain

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 09期

关键词：

Hamiltonian system; generalized 4-D isotropic oscillator; ring-shaped potentials; Liouville-Arnold theorem; periodic orbits; PHASE PORTRAITS; MOTION;

D O I：

10.1142/S0218127410027374

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work we study a generalized integrable biparametric family of 4-D isotropic oscillators. This family allows to treat, in a unified way, oscillators defined by the potentials given by Hartmann and Quesne and other ring-shaped systems. Using the Liouville-Arnold theorem and the analysis of the momentum map in its critical points, we obtain a complete topological classification of the different invariant sets of the phase flow of this problem. By this topological study and the calculation of the action-angle variables we obtain the full classification of periodic and quasiperiodic orbits for this system.

引用

页码：2809 / 2821

页数：13