TITLE:
Dynamical aspects of multi-round horseshoe-shaped
homoclinic orbits in the RTBP
Celestial Mechanics and Dynamical Astronomy (to appear)

AUTHORS:
Esther Barrabes, Josep M. Mondelo, Merce Olle
E-mails: barrabes@ima.udg.edu, jmm@mat.uab.cat, merce.olle@upc.edu


ABSTRACT:
We consider the planar Restricted Three-Body problem 
and the collinear equilibrium point $L_3$, as
an example of a center$\times$saddle equilibrium point
in a Hamiltonian with two degrees of freedom. We explore
the existence of symmetric and non-symmetric homoclinic
orbits to $L_3$, when varying the mass parameter $\mu$.
Concerning the  symmetric homoclinic
orbits (SHO), we study the multi-round,
$m$-round, SHO for $m\ge 2$.
More precisely, given a transversal value of $\mu$
for which there is a 1-round SHO, say $\mu _1$,
we show that for any $m\ge 2$,
there are countable sets of values of $\mu$,
tending to $\mu _1$, corresponding to  m-round SHO.
Some comments on related analytical results are also made.