We prove existence and multiplicity of T-periodic solutions (for any given T) for the N-body problem in R(m) (any m >= 2) where one of the bodies has mass equal to 1 and the others have masses epsilon alpha(2), ... , epsilon alpha(N), epsilon small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass epsilon alpha(i) moves close to one of the circular solutions of the two body problem of period T/k(i), where k(i) is any odd number. No relation has to be satisfied by k(2), ... , k(N).

A Class of Periodic Solutions of the N-body Problem

COTI ZELATI, VITTORIO
1989

Abstract

We prove existence and multiplicity of T-periodic solutions (for any given T) for the N-body problem in R(m) (any m >= 2) where one of the bodies has mass equal to 1 and the others have masses epsilon alpha(2), ... , epsilon alpha(N), epsilon small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass epsilon alpha(i) moves close to one of the circular solutions of the two body problem of period T/k(i), where k(i) is any odd number. No relation has to be satisfied by k(2), ... , k(N).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/466961
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