Highly eccentric hip-hop solutions of the 2N
dc.contributor.author
dc.date.accessioned
2013-02-21T08:07:52Z
dc.date.available
2013-02-21T08:07:52Z
dc.date.issued
2009
dc.identifier.issn
0167-2789
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dc.description.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
dc.format.mimetype
application/pdf
dc.language.iso
eng
dc.publisher
Elsevier
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Versió postprint del document publicat a: http://dx.doi.org/10.1016/j.physd.2009.10.019
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© Physica D: Nonlinear Phenomena, 2010, vol. 239, núm. 3-4, p. 214-219
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Articles publicats (D-IMA)
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Tots els drets reservats
dc.title
Highly eccentric hip-hop solutions of the 2N
dc.type
info:eu-repo/semantics/article
dc.rights.accessRights
info:eu-repo/semantics/openAccess
dc.type.version
info:eu-repo/semantics/acceptedVersion
dc.identifier.doi
dc.identifier.idgrec
011353