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Whiskered parabolic tori in the planar (n+ 1) -body problem
dc.contributor.author | Baldomá Barraca, Inmaculada |
dc.contributor.author | Fontich Julia, Ernest |
dc.contributor.author | Martín de la Torre, Pablo |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2019-11-20T09:05:44Z |
dc.date.available | 2020-07-12T00:25:46Z |
dc.date.issued | 2019-01-01 |
dc.identifier.citation | Baldoma, I.; Fontich Julia, E.; Martin, P. Whiskered parabolic tori in the planar (n+ 1) -body problem. "Communications in mathematical physics", 1 Gener 2019. |
dc.identifier.issn | 0010-3616 |
dc.identifier.uri | http://hdl.handle.net/2117/172724 |
dc.description | “This is a post-peer-review, pre-copyedit version of an article published in Communications in mathematical physics. The final authenticated version is available online at: https://dx.doi.org/10.1007/s00220-019-03507-3 |
dc.description.abstract | The planar (n+1)-body problem models the motion of n+1 bodies in the plane under their mutual Newtonian gravitational attraction forces. When n=3, the question about final motions, that is, what are the possible limit motions in the planar (n+1)-body problem when t¿8, ceases to be completely meaningful due to the existence of non-collision singularities. In this paper we prove the existence of solutions of the planar (n+1)-body problem which are defined for all forward time and tend to a parabolic motion, that is, that one of the bodies reaches infinity with zero velocity while the rest perform a bounded motion. These solutions are related to whiskered parabolic tori at infinity, that is, parabolic tori with stable and unstable invariant manifolds which lie at infinity. These parabolic tori appear in cylinders which can be considered “normally parabolic”. The existence of these whiskered parabolic tori is a consequence of a general theorem on parabolic tori developed in this paper. Another application of our theorem is a conjugation result for a class of skew product maps with a parabolic torus with its normal form generalizing results of Takens (Ann Inst Fourier 23(2):163–195, 1973), and Voronin (Funktsional Anal i Prilozhen 15(1):1–17, 96, 1981). |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Many-body problem |
dc.subject.lcsh | Hamiltonian systems |
dc.title | Whiskered parabolic tori in the planar (n+ 1) -body problem |
dc.type | Article |
dc.subject.lemac | Problema dels cossos múltiples |
dc.subject.lemac | Sistemes hamiltonians |
dc.contributor.group | Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC |
dc.identifier.doi | 10.1007/s00220-019-03507-3 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | https://link.springer.com/article/10.1007%2Fs00220-019-03507-3 |
dc.rights.access | Open Access |
local.identifier.drac | 25816371 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Baldoma, I.; Fontich Julia, Ernest; Martin, P. |
local.citation.publicationName | Communications in mathematical physics |
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