Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

Authors: Maciejewski, A.¹; Rybicki, S.²

Source: Celestial Mechanics and Dynamical Astronomy, Volume 88, Number 3, March 2004 , pp. 293-324(32)

Publisher: Springer

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Abstract:

We describe global bifurcations from the libration points of non-stationary periodic solutions of the restricted three body problem. We show that the only admissible continua of non-stationary periodic solutions of the planar restricted three body problem, bifurcating from the libration points, can be the short-period families bifurcating from the Lagrange equilibria L ₄^μ, L ₅^μ. We classify admissible continua and show that there are possible exactly six admissible continua of non-stationary periodic solutions of the planar restricted three body problem. We also characterize admissible continua of non-stationary periodic solutions of the spatial restricted three body problem. Moreover, we combine our results with the Déprit and Henrard conjectures (see [8]), concerning families of periodic solutions of the planar restricted three body problem, and show that they can be formulated in a stronger way. As the main tool we use degree theory for SO(2)-equivariant gradient maps defined by the second author in [25].

Keywords: degree theory for SO(2)-equivariant orthogonal map; global bifurcations of periodic solutions; restricted three body problem

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:CELE.0000017193.10060.ac

Affiliations: 1: Institute of Astronomy, University of Zielona Góra, Podgórna 50, 65-246, Zielona Góra, Poland, Email: maciejka@astro.ia.uz.zgora.pl 2: Faculty of Mathematics and Computer Science, Nicolaus, Copernicus University, PL-87-100, Toruń, ul. Chopina 12/18, Poland, Email: Slawomir.Rybicki@mat.uni.torun.pl

Publication date: 2004-03-01