112 research outputs found
Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - A Computer Assisted Proof
The restricted circular three-body problem is considered for the following
parameter values , - the values for {\em Oterma} comet
in the Sun-Jupiter system.
We present a computer assisted proof of an existence of homo- and
heteroclinic cycle between two Lyapunov orbits and an existence of symbolic
dynamics on four symbols built on this cycle.Comment: 40 pages, 11 figure
Transition Tori in the Planar Restricted Elliptic Three Body Problem
We consider the elliptic three body problem as a perturbation of the circular
problem. We show that for sufficiently small eccentricities of the elliptic
problem, and for energies sufficiently close to the energy of the libration
point L2, a Cantor set of Lyapounov orbits survives the perturbation. The
orbits are perturbed to quasi-periodic invariant tori. We show that for a
certain family of masses of the primaries, for such tori we have transversal
intersections of stable and unstable manifolds, which lead to chaotic dynamics
involving diffusion over a short range of energy levels. Some parts of our
argument are nonrigorous, but are strongly backed by numerical computations
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