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 (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.

Mathematics Subject Classification: 70F07, 70H12, 34C30, 34C37

Print publication: Issue 9 (September 2006)
Received 8 December 2005, in final form 5 July 2006
Published 27 July 2006