4:00 pm Wednesday, October 27, 2010
Working Dynamical Systems: Transition tori in the planar restricted elliptic three body problem by M. Capinski (Jagiellonian University/U.T. Austin) in RLM 10.176
In the circular restricted three body problem, around libration fixed points there exist families of periodic orbits, called Lyapunov orbits, which are parameterized by energy. The stable and unstable manifolds of these orbits have transversal intersections. We shall show that when the elliptic three body problem is considered as a perturbation of the circular problem, then under appropriate conditions the family of Lyapunov orbits is perturbed to a family of two dimensional KAM tori in the extended phase space. We shall also show that the stable and unstable manifolds associated to the surviving tori intersect transversally for tori perturbed from Lyapunov orbits with sufficiently close energies. Such intersections lead to dynamics similar to Arnold diffusion, but involving short ranges of energies. Submitted by
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