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Hamiltonian Mechanics pp 385–390Cite as

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

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Part of the book series: NATO ASI 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

This research was partially supported by the Russian Fund of Fundamental Researches under grant N93 — 011 — 1787.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Institute for Water Transport Engineers, 5, Nesterov str., Nizhny Novgorod, 603600, Russia

    O. Yu. Koltsova

  2. Research Institute for Applied Math.& Cybernetics, 10, Ul’yanov str., Nizhny Novgorod, 603600, Russia

    Lev M. Lerman

Authors
  1. O. Yu. Koltsova
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  2. Lev M. Lerman
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Editor information

Editors and Affiliations

  1. University of the Aegean, Samos, Greece

    John Seimenis

  2. N. Copernicus University, Torun, Poland

    John Seimenis

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© 1994 Springer Science+Business Media New York

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Koltsova, O.Y., Lerman, L.M. (1994). Dynamics and Bifurcations in Two-Parameter Unfolding of a Hamiltonian System with a Homoclinic Orbit to a Saddle-Center. In: Seimenis, J. (eds) Hamiltonian Mechanics. NATO ASI Series, vol 331. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0964-0_41

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  • DOI: https://doi.org/10.1007/978-1-4899-0964-0_41

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-0966-4

  • Online ISBN: 978-1-4899-0964-0

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