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

E. Barrabés, J. M. Mondelo, M. Ollé

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7 Citations (Scopus)

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 languageEnglish
Pages (from-to)197-210
JournalCelestial Mechanics and Dynamical Astronomy
Volume105
Issue number1
DOIs
Publication statusPublished - 1 Oct 2009

Keywords

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

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