HOMOCLINIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

Acta mathematica scientia,Series B ›› 1996, Vol. 16 ›› Issue (4): 361-374.

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HOMOCLINIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

Zhao Xiaohua¹, Li Jibin², Huang Kelei³

1. Dept. of Math. Of Yunnan University, Kunming 650091, China;
2. Institute of Appl. Math. of Yunnan Province, Kunming 650091, China;
2. Beijing University of Aero. and Astro., Beijing 100083, China

Received:1993-04-16 Revised:1994-12-19 Online:1996-12-25 Published:1996-12-25
Supported by:
The project supported by the NNSF of China and the STCF of Yunnan Province.

Abstract

Abstract: It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds.Thed we apply them to a truncated spectral model of the quasi-geostrophic flow on a cyclic β-plane.

Key words: bifurcation, Poisson bracket, Generalized Hamiltonian system, homoclinic orbit, Melnikov method, perturbation theory

Zhao Xiaohua, Li Jibin, Huang Kelei. HOMOCLINIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS[J].Acta mathematica scientia,Series B, 1996, 16(4): 361-374.

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HOMOCLINIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

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