Esther Barrabés and Mercè Ollé 2006 Nonlinearity 19 2065 doi:10.1088/0951-7715/19/9/004
Invariant manifolds of L3 and horseshoe motion in the restricted three-body problem
Esther Barrabés1 and Mercè Ollé2
Show affiliationsRecommended by A Chenciner
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 (HPOs) (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 HPOs 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 analysed. Finally, the relationship between the horseshoe homoclinic orbits and the HPO is considered in detail.
- PACS
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02.40.Sf Manifolds and cell complexes
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
- MSC
- Subjects
- Dates
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Issue 9 (September 2006)
Received 8 December 2005, in final form 5 July 2006
Published 27 July 2006
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Invariant manifolds of L3 and horseshoe motion in the restricted three-body problem
Esther Barrabés and Mercè Ollé 2006 Nonlinearity 19 2065
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