Invariant manifolds of L_3 and horseshoe motion in the restricted three-body problem
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Tipus de documentArticle
Data publicació2005
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 2.5 Espanya
Abstract
In this paper, we consider horseshoe motion in the planar restricted three-body
problem. On one hand, we deal with the families of horseshoe periodic orbits (which
surround three equilibrium points called L3, L4 and L5), when the mass parameter
µ is positive and small; we describe the structure of such families from the two-body
problem (µ = 0). On the other hand, the region of existence of horseshoe periodic
orbits for any value of µ ∈ (0, 1/2] implies the understanding of the behaviour of the
invariant manifolds of L3. So, a systematic analysis of such manifolds is carried out.
As well the implications on the number of homoclinic connections to L3, and on the
simple infinite and double infinite period homoclinic phenomena are also analysed.
Finally, the relationship between the horseshoe homoclinic orbits and the horseshoe
periodic orbits are considered in detail.
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