Chinese Annals of Mathematics, Series B

, Volume 28, Issue 1, pp 81–92

Bifurcation of Homoclinic Orbits with Saddle-Center Equilibrium*


    • Department of MathematicsEast China Normal University
  • Xianlong Fu
    • Department of MathematicsEast China Normal University
  • Deming Zhu
    • Department of MathematicsEast China Normal University

DOI: 10.1007/s11401-005-0226-5

Cite this article as:
Liu, X., Fu, X. & Zhu, D. Chin. Ann. Math. Ser. B (2007) 28: 81. doi:10.1007/s11401-005-0226-5


In this paper, the authors develop new global perturbation techniques for detecting the persistence of transversal homoclinic orbits in a more general nondegenerated system with action-angle variable. The unperturbed system is assumed to have saddlecenter type equilibrium whose stable and unstable manifolds intersect in one dimensional manifold, and does not have to be completely integrable or near-integrable. By constructing local coordinate systems near the unperturbed homoclinic orbit, the conditions of existence of transversal homoclinic orbit are obtained, and the existence of periodic orbits bifurcated from homoclinic orbit is also considered.


Local coordinate systemHomoclinic orbitBifurcation

2000 MR Subject Classification

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© Springer-Verlag Berlin Heidelberg 2007