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

• Articles •     Next Articles

HOMOCLINIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

Zhao Xiaohua1, Li Jibin2, Huang Kelei3   

  1. 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.

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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

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