PERIODIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (4): 370-384.

PERIODIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

赵晓华¹, 李继彬², 黄克累³

1. Dept. of Math. of Yunnan Unly. & Iust. of Appl. Math. of Yunnan Province, Yunnan 650091, China;
2. Institute of Appl. Math. of Yunnan Province, Yunnan 650091, China;
3. Beijing University of Aero. & Astro., Beijing 100083, China

收稿日期:1993-04-16 出版日期:1995-12-25 发布日期:1995-12-25
基金资助:
The project supported by the NNSF of China and the STCF of Yunnan Province.

PERIODIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

Zhao Xiaohua¹, Li Jibin², Huang Kelei³

1. Dept. of Math. of Yunnan Unly. & Iust. of Appl. Math. of Yunnan Province, Yunnan 650091, China;
2. Institute of Appl. Math. of Yunnan Province, Yunnan 650091, China;
3. Beijing University of Aero. & Astro., Beijing 100083, China

Received:1993-04-16 Online:1995-12-25 Published:1995-12-25
Supported by:
The project supported by the NNSF of China and the STCF of Yunnan Province.

摘要/Abstract

摘要： In this paper, we develop a global perturbation technique for the study of periodic orbits in three-dimensional, time dependent and independent, perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds. We give existence, stability and bifurcation theorems and illustrate our results with a truncated spectral model of the forced, dissipative quasi-geostrophic flow on a cyclic β-plane.

关键词: Generalized Hamiltonian system, periodic orbit, Melnikov method

Abstract: In this paper, we develop a global perturbation technique for the study of periodic orbits in three-dimensional, time dependent and independent, perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds. We give existence, stability and bifurcation theorems and illustrate our results with a truncated spectral model of the forced, dissipative quasi-geostrophic flow on a cyclic β-plane.

Key words: Generalized Hamiltonian system, periodic orbit, Melnikov method

赵晓华, 李继彬, 黄克累. PERIODIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS[J]. 数学物理学报(英文版), 1995, 15(4): 370-384.

Zhao Xiaohua, Li Jibin, Huang Kelei. PERIODIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS[J]. Acta mathematica scientia,Series B, 1995, 15(4): 370-384.

[1]	夏红强; 葛云飞; 张正杰. EQUIDISTRIBUTION OF CLOSED ORBITS OF BILLIARD FLOWS ON THE PLANE[J]. 数学物理学报(英文版), 2007, 27(3): 465-472.
[2]	赵晓华, 李继彬, 黄克累. HOMOCLINIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS[J]. 数学物理学报(英文版), 1996, 16(4): 361-374.

PERIODIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

PERIODIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

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