Invariant manifolds at infinity of the RTBP and the boundaries of bounded motion

Regina Martínez, Carles Simó

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

© 2014, Pleiades Publishing, Ltd. Invariant manifolds of a periodic orbit at infinity in the planar circular RTBP are studied. To this end we consider the intersection of the manifolds with the passage through the barycentric pericenter. The intersections of the stable and unstable manifolds have a common even part, which can be seen as a displaced version of the two-body problem, and an odd part which gives rise to a splitting. The theoretical formulas obtained for a Jacobi constant C large enough are compared to direct numerical computations showing improved agreement when C increases. A return map to the pericenter passage is derived, and using an approximation by standard-like maps, one can make a prediction of the location of the boundaries of bounded motion. This result is compared to numerical estimates, again improving for increasing C. Several anomalous phenomena are described.
Original languageEnglish
Pages (from-to)745-765
JournalRegular and Chaotic Dynamics
Volume19
Issue number6
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • invariant rotational curves
  • restricted three-body problem
  • separatrix maps
  • splitting function

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