Families of double symmetric "Schubart-like" periodic orbits

Regina Martínez

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

We consider a class of Hamiltonian systems with two degrees of freedom with singularities. This class includes several symmetric subproblems of the n-body problem where the singularities are due to collisions involving two or more bodies. "Schubart-like" periodic orbits having two collisions in one period, are present in most of these subproblems. The purpose of this paper is to study the existence of families of such a periodic orbits in a general setting. The blow up techniques of total collision and infinity are applied to our class of Hamiltonian system. This allows us to derive sufficient conditions to ensure the existence of families of double symmetric "Schubart-like" periodic orbits having many singularities. The orbits in the family can be parametrized by the number of singularities in one period. The results are applied to some subproblems of the gravitational n-body problem. © 2013 Springer Science+Business Media Dordrecht.
Original languageEnglish
Pages (from-to)217-243
JournalCelestial Mechanics and Dynamical Astronomy
Volume117
Issue number3
DOIs
Publication statusPublished - 1 Nov 2013

Keywords

  • Collisions
  • DSSP orbits
  • n-body problem
  • Symmetric periodic orbits

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