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Títol:	Highly eccentric hip-hop solutions of the 2N
Autor/a:	Barrabés Vera, Esther; Cors, Josep M.; Pinyol i Pérez, Concepció; Soler, Jaume
Abstract:	We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ϵ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ϵ ≠ 0, the topological transversality persists and Brouwer's fixed point theorem shows the existence of this kind of solutions in the full system
Matèries:	-Topologia -Topology -Poliedres -Polyhedra
Drets:	Tots els drets reservats
Tipus de document:	Article Article - Versió acceptada
Publicat per:	Elsevier
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