On Families of Periodic Orbits in the Restricted Three-Body Problem

• Kim, Seongchan ^[1]
  1. [1] University of Augsburg

     University of Augsburg

     Kreisfreie Stadt Augsburg, Alemania

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 1, 2019, págs. 201-232
• Idioma: inglés
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• Resumen

  • Since Poincaré, periodic orbits have been one of the most important objects in dynamical systems. However, searching them is in general quite difficult. A common way to find them is to construct families of periodic orbits which start at obvious periodic orbits. On the other hand, given two periodic orbits one might ask if they are connected by an orbit cylinder, i.e., by a one-parameter family of periodic orbits. In this article we study this question for a certain class of periodic orbits in the planar circular restricted three-body problem. Our strategy is to compare the Cieliebak–Frauenfelder–van Koert invariants which are obstructions to the existence of an orbit cylinder.