Dynamical aspects of multi-round horseshoe-shaped homoclinic orbits in the RTBP

Abstract

We consider the planar restricted three-body problem and the collinear equilibrium point L3, as an example of a center×saddle equilibrium point in a Hamiltonian with two degrees of freedom.We explore numerically the existence of symmetric and non-symmetric homoclinic orbits to L3, when varying the mass parameter μ. Concerning the symmetric homoclinic orbits (SHO), we study the multi-round, m-round, SHO for m ≥ 2. More precisely, given a transversal value of μ for which there is a 1-round SHO, say μ1, we show that for any m ≥ 2, there are countable sets of values of μ, tending to μ1, corresponding to m-round SHO. Some comments on related analytical results are also made.