Periodic Orbits Near a Heteroclinic Loop Formed by One-Dimensional Orbit and a Two-Dimensional Manifold: Application to the Charged Collinear Three-Body Problem

Llibre, J.; PaŞCa, D.

International Journal of Bifurcation and Chaos 17(06): 2175-2183


ISSN/ISBN: 0218-1274
Accession: 086540954

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This paper is devoted to the study of a type of differential systems which appear usually in the study of the Hamiltonian systems with two degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near to the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear three-body problem.