Dynamics and Bifurcations in Two-Parameter Unfolding of a Hamiltonian System with a Homoclinic Orbit to a Saddle-Center

  • O. Yu. Koltsova
  • Lev M. Lerman
Part of the NATO ASI Series book series (NSSB, volume 331)


Our goal in this paper is to present some elements of global behavior of Hamiltonian systems with two degrees of freedom in a vicinity of a homoclinic orbit to a saddle-center equilibrium point. Besides of a pure mathematical interest such structure (i.e., a homoclinic orbit to a saddle-center) is surprisingly often encountered in different problems ranging from celestial mechanics (doubly-asymptotic orbits to collinear libration points1,2) to modern problems of mathematical physics.3


Periodic Orbit Hamiltonian System Homoclinic Orbit Integrable Hamiltonian System Hamiltonian Vector Field 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • O. Yu. Koltsova
    • 1
  • Lev M. Lerman
    • 2
  1. 1.Department of MathematicsInstitute for Water Transport EngineersNizhny NovgorodRussia
  2. 2.Research Institute for Applied Math.& CyberneticsNizhny NovgorodRussia

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