Invariant tori of rectilinear type in the spatial three-body problem

Palacián Subiela, Jesús Francisco; Sayas Bordonaba, Flora; Yanguas Sayas, Patricia

Invariant tori of rectilinear type in the spatial three-body problem

dc.contributor.author	Palacián Subiela, Jesús Francisco
dc.contributor.author	Sayas Bordonaba, Flora
dc.contributor.author	Yanguas Sayas, Patricia
dc.contributor.department	Estadística, Informática y Matemáticas	es_ES
dc.contributor.department	Estatistika, Informatika eta Matematika	eu
dc.contributor.department	Institute for Advanced Materials and Mathematics - INAMAT2	en
dc.date.accessioned	2024-06-18T18:05:48Z
dc.date.available	2024-06-18T18:05:48Z
dc.date.issued	2024
dc.date.updated	2024-06-18T17:53:31Z
dc.description.abstract	In the context of the spatial three-body problem and KAM theory, specifically in the regime where the Hamiltonian function is split as the sum of two Keplerian terms plus a small perturbation, we deal with quasi-periodic motions of the three bodies such that two of the three particles (the so-called inner bodies) describe near-collision orbits. More precisely the inner bodies never collide, but they follow orbits that are bounded straight lines or close to straight lines. The motion of the inner bodies occurs either near the axis that is perpendicular to the invariable plane (i.e. the fixed plane orthogonal to the angular momentum vector that passes through the centre of mass of the system) or near the invariable plane. The outer particle’s trajectory has an eccentricity varying between zero and a value that is upper bounded by eM 2 < 1 and lies near the invariable plane. The three bodies’ orbits fill in invariant 5-tori and when the inner particles move in an axis perpendicular to the invariable plane, they correspond to new solutions of the three-body problem. Our approach consists in a combination of a regularisation procedure with the construction of various reduced spaces and the explicit determination of sets of symplectic coordinates. The various reduced spaces we build depend on what symmetries are taken into consideration for the reduction. Moreover we apply an iso-energetic theorem by Han, Li and Yi on the persistence of quasi-periodic solutions for Hamiltonian systems with high-order proper degeneracy. All these elements allow us to calculate explicitly the torsions for the possible combinations that the three particles’ motions can achieve	en
dc.description.sponsorship	The authors have received partial support by Projects MTM 2011-28227-C02-01 of the Ministry of Science and Innovation of Spain; MTM 2014-59433-C2-1-P of the Ministry of Economy and Competitiveness of Spain; and MTM 2017-88137-C2-1-P of the Ministry of Economy, Industry and Competitiveness of Spain.	en
dc.format.mimetype	application/pdf	en
dc.format.mimetype	application/mathematica	en
dc.identifier.citation	Palacián, J. F., Sayas, F., Yanguas, P. (2024) Invariant tori of rectilinear type in the spatial three-body problem. Journal of Differential Equations, 399, 82-180. https://doi.org/10.1016/j.jde.2024.03.008.	en
dc.identifier.doi	10.1016/j.jde.2024.03.008
dc.identifier.issn	0022-0396
dc.identifier.uri	https://academica-e.unavarra.es/handle/2454/48394
dc.language.iso	eng	en
dc.publisher	Elsevier	en
dc.relation.ispartof	Journal of Differential Equations 399, (2024), 82–180	en
dc.relation.projectID	info:eu-repo/grantAgreement/MICINN//MTM2011-28227-C02-01/ES/
dc.relation.projectID	info:eu-repo/grantAgreement/MINECO//MTM2014-59433-C2-1-P/ES/
dc.relation.projectID	info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88137-C2-1-P/ES/
dc.relation.publisherversion	https://doi.org/10.1016/j.jde.2024.03.008
dc.rights	© 2024 The Author(s). This is an open access article under the CC BY license.	en
dc.rights.accessRights	info:eu-repo/semantics/openAccess
dc.rights.uri	https://creativecommons.org/licenses/by/4.0/
dc.subject	Spatial three-body problem	en
dc.subject	Integrals and symmetries	en
dc.subject	Regular and singular reductions	en
dc.subject	Regularisation of the inner double collisions	en
dc.subject	Quasi-periodic motions of rectilinear type	en
dc.subject	KAM theory for properly degenerate Hamiltonians	en
dc.title	Invariant tori of rectilinear type in the spatial three-body problem	en
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/publishedVersion
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