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Symmetric Homoclinic Orbits at the Periodic Hamiltonian Hopf Bifurcation

Department of Differential Equations and Mathematical Analysis, N. I. Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., Nizhny Novgorod 603950, Russia

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and

Anna Markova

Department of Differential Equations and Mathematical Analysis, N. I. Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., Nizhny Novgorod 603950, Russia

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https://doi.org/10.1142/S0218127414400069Cited by:2 (Source: Crossref)

Abstract

We prove the existence of symmetric homoclinic orbits to a saddle-focus symmetric periodic orbit that appears in a generic family of reversible three degrees of freedom Hamiltonian system due to periodic Hamiltonian Hopf bifurcation, if some coefficient A of the normal form of the fourth order is positive. If this coefficient is negative, then for the opposite side of the bifurcation parameter value, we prove the existence of symmetric homoclinic orbits to saddle invariant 2-tori.

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