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October  2004, 11(4): 745-755. doi: 10.3934/dcds.2004.11.745

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, Italy

Received  January 2003 Revised  December 2003 Published  September 2004

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.
Keywords: periodic solutions, Restricted 3-body problem, linear stability.
Mathematics Subject Classification: 34C25, 35B10, 37J4.
Citation: Gianni Arioli. Branches of periodic orbits for the planar restricted 3-body problem. Discrete and Continuous Dynamical Systems, 2004, 11 (4) : 745-755. doi: 10.3934/dcds.2004.11.745
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