This article is cited in 5 papers

Families of multi-round homoclinic and periodic orbits near a saddle-center equilibrium

O. Yu. Koltsova

Dept. of Comput. Math. and Cybernetics, Nizhny Novgorod State University, 23 Gagarin Ave., 603600 Nizhny Novgorod, Russia

Abstract: We consider a real analytic two degrees of freedom Hamiltonian system possessing a homoclinic orbit to a saddle-center equilibrium $p$ (two nonzero real and two nonzero imaginary eigenvalues). We take a two-parameter unfolding for such a system and show that in the case of nonresonance there are countable sets of multi-round homoclinic orbits to $p$. We also find families of periodic orbits, accumulating a the homoclinic orbits.

MSC: 37J45, 37G99

Received: 17.12.2002

Language: English

DOI: 10.1070/RD2003v008n02ABEH000240

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