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. © Springer Science+Business Media B.V. 2009.
Original language | English |
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Pages (from-to) | 197-210 |
Journal | Celestial Mechanics and Dynamical Astronomy |
Volume | 105 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Oct 2009 |
Keywords
- Homoclinic connection to L3
- Invariant manifolds
- Multi-round homoclinic orbits
- Restricted three-body problem
- Symmetric homoclinic orbits