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Preprints of the Keldysh Institute of Applied Mathematics, 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.
Document Type: Preprint
Language: Russian
Citation: A. D. Bruno, V. P. Varin, “Complicated families of periodic solutions of the restricted problem”, Keldysh Institute preprints, 2007, 035, 18 pp.
Citation in format AMSBIB
\Bibitem{BruVar07}
\by A.~D.~Bruno, V.~P.~Varin
\paper Complicated families of periodic solutions of the restricted problem
\jour Keldysh Institute preprints
\yr 2007
\papernumber 035
\totalpages 18
\mathnet{http://mi.mathnet.ru/ipmp490}
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    Препринты Института прикладной математики им. М. В. Келдыша РАН
     
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