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

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

Nov 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cemda.105..197b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 105, Issue 1-3, pp. 197-210

Astronomy and Astrophysics

Astronomy

2

Scientific paper

We consider the planar restricted three-body problem and the collinear equilibrium point L 3, 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 L 3, 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 μ 1, we show that for any m ≥ 2, there are countable sets of values of μ, tending to μ 1, corresponding to m-round SHO. Some comments on related analytical results are also made.

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