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A class of periodic solutions of the N-body problem
Authors:Vittorio Coti Zelati
Institution:(1) CEREMADE, Université de Paris Dauphine, UA CNRS no 749, Place du M. de Lattre de Tassigny, 75575 Paris Cedex 16, France;(2) Present address: SISSA, strada Costiera, 11, 34014 Trieste, Italy
Abstract:We prove existence and multiplicity of T-periodic solutions (for any given T) for the N-body problem in Ropf m (any m ges 2) where one of the bodies has mass equal to 1 and the others have masses epsiagr2,...,isinagr N , epsi small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass epsiagri moves close to one of the circular solutions of the two body problem of period T/k i, where ki is any odd number. No relation has to be satisfied by k 2,...,k N.
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