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KIAM Preprint № 35, Moscow, 2007
Authors: Bruno A. D., Varin V. P.
Complicated Families of Periodic Solutions of the Restricted Problem
Abstract:
We consider the plane circular restricted three-body problem for small mass ratios μ of principal bodies. Here we continue the study of families of periodic solutions which we begun in Preprint 'Periodic solutions of the restricted three-body problem for small μ '. Using generating families, for small μ > 0, we studied the family i which begins as direct circular orbits of infinitely small radius around the body of bigger mass. We demonstrated that, as μ increases, the structure of the family i undergoes infinitely many bifurcations with the birth of infinitely many closed subfamilies, each of which exists only in some interval of values of μ. In addition, we give the theory of generation of shoe-like orbits and orbits in the form of 'tadpoles'; we present the structure of principal families containing periodic solutions with these orbits.
Publication language: russian,  pages: 18
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Bruno Alexander Dmitrievich,  orcid.org/0000-0002-7465-1258KIAM RAS
  • Varin Victor Petrovich,  orcid.org/0000-0001-7324-1823KIAM RAS