Infinitely many periodic orbits for the octahedral 7-body problem

Montserrat Corbera; Jaume Llibre

doi:https://doi.org/10.1007/s12346-008-0005-2

Infinitely many periodic orbits for the octahedral 7-body problem

Montserrat Corbera, Jaume Llibre

Department of Mathematics

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

Abstract

We prove the existence of infinitely many symmetric periodic orbits for a regularized octahedral 7-body problem with six small masses placed at the vertices of an octahedron centered in the seventh mass. The main tools for proving the existence of such periodic orbits is the analytic continuation method together with the symmetry of the problem. © 2008 Birkhäuser Verlag Basel/Switzerland.

Original language	English
Pages (from-to)	101-122
Journal	Qualitative Theory of Dynamical Systems
Volume	7
DOIs	https://doi.org/10.1007/s12346-008-0005-2
Publication status	Published - 1 Aug 2008

Keywords

7-body problem
Continuation method
Symmetric periodic orbits

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abstract = "We prove the existence of infinitely many symmetric periodic orbits for a regularized octahedral 7-body problem with six small masses placed at the vertices of an octahedron centered in the seventh mass. The main tools for proving the existence of such periodic orbits is the analytic continuation method together with the symmetry of the problem. {\textcopyright} 2008 Birkh{\"a}user Verlag Basel/Switzerland.",

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AU - Corbera, Montserrat

AU - Llibre, Jaume

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N2 - We prove the existence of infinitely many symmetric periodic orbits for a regularized octahedral 7-body problem with six small masses placed at the vertices of an octahedron centered in the seventh mass. The main tools for proving the existence of such periodic orbits is the analytic continuation method together with the symmetry of the problem. © 2008 Birkhäuser Verlag Basel/Switzerland.

AB - We prove the existence of infinitely many symmetric periodic orbits for a regularized octahedral 7-body problem with six small masses placed at the vertices of an octahedron centered in the seventh mass. The main tools for proving the existence of such periodic orbits is the analytic continuation method together with the symmetry of the problem. © 2008 Birkhäuser Verlag Basel/Switzerland.

KW - 7-body problem

KW - Continuation method

KW - Symmetric periodic orbits

U2 - https://doi.org/10.1007/s12346-008-0005-2

DO - https://doi.org/10.1007/s12346-008-0005-2

M3 - Article

VL - 7

SP - 101

EP - 122

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

SN - 1575-5460

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