On Hamiltonian Systems with a Homoclinic Orbit to a Saddle-Center |
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Authors: | O Yu Koltsova |
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Institution: | (1) Research Institute of Applied Mathematics and Cybernetics, Nizhnii Novgorod State University, Nizhnii Novgorod, Russia |
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Abstract: | We consider a real analytic Hamiltonian system with two degrees of freedom having a homoclinic orbit to a saddle-center equilibrium (two nonzero real and two nonzero imaginary eigenvalues). We take a two-parameter unfolding for such a system and show that in the nonresonance case, there are countable sets of multi-round homoclinic orbits to a saddle-center. We also find families of periodic orbits accumulating at homoclinic orbits. Bibliography: 6 titles.__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 300, 2003, pp. 187–193. |
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