Periodic orbits near a heteroclinic loop formed by one-dimensional orbit and a two-dimensional manifold: Application to the charged collinear three-body problem

Jaume Llibre; Daniel Paşca

doi:https://doi.org/10.1142/S0218127407018312

Periodic orbits near a heteroclinic loop formed by one-dimensional orbit and a two-dimensional manifold: Application to the charged collinear three-body problem

Jaume Llibre, Daniel Paşca

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

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. AU 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. © World Scientific Publishing Company.

Original language	English
Pages (from-to)	2175-2183
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	17
DOIs	https://doi.org/10.1142/S0218127407018312
Publication status	Published - 1 Jan 2007

Keywords

Charged 3-body problem
Heteroclinic loop
Periodic orbits

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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, Jaume; Paşca, Daniel.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 17, 01.01.2007, p. 2175-2183.

Research output: Contribution to journal › Article › Research › peer-review

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AU - Paşca, Daniel

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AB - 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. AU 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. © World Scientific Publishing Company.

KW - Charged 3-body problem

KW - Heteroclinic loop

KW - Periodic orbits

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