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Discrete Contin. Dyn. Syst. Ser. A, 2013, Volume 33, Issue 3, Pages 1009–1032 (Mi dcds2)  

Variational approach to second species periodic solutions of Poincaré three-body problem

S. V. Bolotinab, P. Negrinic

a Department of Mathematics, University of Wisconsin, Madison, United States
b Steklov Mathematical Institute of Russian Academy of Sciences
c Department of Mathematics, La Sapienza, University of Rome, Italy

Abstract: We consider the plane 3 body problem with 2 of the masses small. Periodic solutions with near collisions of small bodies were named by Poincaré second species periodic solutions. Such solutions shadow chains of collision orbits of 2 uncoupled Kepler problems. Poincaré only sketched the proof of the existence of second species solutions. Rigorous proofs appeared much later and only for the restricted 3 body problem. We develop a variational approach to the existence of second species periodic solutions for the nonrestricted 3 body problem. As an application, we give a rigorous proof of the existence of a class of second species solutions.

DOI: https://doi.org/10.3934/dcds.2013.33.1009


Bibliographic databases:

Document Type: Article
MSC: 70F10, 70F15, 37N05
Received: 01.04.2011
Revised: 01.02.2012
Language: English

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