Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

Details Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

Mar 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cemda..88..293m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 88, Issue 3, p. 293-324 (2004).

Astronomy and Astrophysics

Astronomy

3

Degree Theory For So(2)-Equivariant Orthogonal Maps, Global Bifurcations Of Periodic Solutions, Restricted Three Body Problem

Scientific paper

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 4μ, L 5μ. 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].

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