Branches of periodic orbits for the planar restricted 3-body problem

Gianni Arioli

doi:10.3934/dcds.2004.11.745

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2004, Volume 11, Issue 4: 745-755. Doi: 10.3934/dcds.2004.11.745

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Branches of periodic orbits for the planar restricted 3-body problem

Gianni Arioli^1,

1.
Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano

Received: January 2003

Revised: December 2003

Published: October 2004

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Abstract

We describe a method for studying the existence and the linear stability of branches of periodic solutions for a dynamical system with a parameter. We apply the method to the planar restricted 3-body problem extending the results of [A]. More precisely, we prove the existence of some continuous branches of periodic orbits with the energy or the masses of the primaries as parameters, and provide an approximation of the orbits with rigorous bounds. We prove the linear stability or instability of the orbits.

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Mathematics Subject Classification: 34C25, 35B10, 37J45.

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