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JOURNALS // Preprints of the Keldysh Institute of Applied Mathematics // Archive

Keldysh Institute preprints, 2007 035, 18 pp. (Mi ipmp490)

Complicated families of periodic solutions of the restricted problem

A. D. Bruno, V. P. Varin


Abstract: We consider the plane circular restricted three-body problem for small mass ratios $\mu$ 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 $\mu$". Using generating families, for small $\mu>0$, 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 $\mu$ 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 $\mu$. 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.



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