Celestial Mechanics and Dynamical Astronomy

, Volume 105, Issue 1–3, pp 197–210 | Cite as

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

Original Article


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.


Invariant manifolds Multi-round homoclinic orbits Restricted three-body problem Symmetric homoclinic orbits Homoclinic connection to L3 


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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Departament d’Informàtica i Matemàtica AplicadaUniversitat de GironaGironaSpain
  2. 2.IEEC and Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain
  3. 3.Departament de Matemàtica Aplicada IUniversitat Politècnica de CatalunyaBarcelonaSpain

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