Global Bifurcations of Periodic solutions of the Hill Lunar Problem*

Astronomy and Astrophysics – Astronomy

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Autonomous Hamiltonian Systems, Bifurcation Index, Global Bifurcations Of Periodic Solutions

Scientific paper

We describe global bifurcations of non-stationary periodic solutions of the Hill Lunar Problem. Especially we are interested in description of closed connected sets (continua) of non-stationary periodic solutions which bifurcate from stationary ones. Such continua of solutions of the Hill Lunar Problem are not admissible in H^1_2π\Λ(H). For the Regularized Hill Lunar Problem we prove that these families are unbounded in H^1_2π. As the main tool we use degree theory for SO(2)-equivariant orthogonal maps defined by S.M. Rybicki.

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