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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)

Abstract

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

Keywords

Periodic Orbit Hamiltonian System Homoclinic Orbit Integrable Hamiltonian System Hamiltonian Vector Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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