Normalization through invariants in n-dimensional Kepler problems

View/ Open
Date
2018Version
Acceso abierto / Sarbide irekia
xmlui.dri2xhtml.METS-1.0.item-type
Artículo / Artikulua
Version
Versión aceptada / Onetsi den bertsioa
Project Identifier
ES/1PE/MTM2014-59433 ES/2PE/MTM2017-88137
Impact
|
10.1134/S1560354718040032
Abstract
We present a procedure for the normalization of perturbed Keplerian problems in n dimensions based on Moser regularization of the Kepler problem and the invariants associated to the reduction process. The approach allows us not only to circumvent the problems introduced by certain classical variables used in the normalization of this kind of problems, but also to do both the normalization and red ...
[++]
We present a procedure for the normalization of perturbed Keplerian problems in n dimensions based on Moser regularization of the Kepler problem and the invariants associated to the reduction process. The approach allows us not only to circumvent the problems introduced by certain classical variables used in the normalization of this kind of problems, but also to do both the normalization and reduction in one step. The technique is introduced for any dimensions and is illustrated for n = 2, 3 by relating Moser coordinates with Delaunay-like variables. The theory is applied to the spatial circular restricted three-body problem for the study of the existence of periodic and quasi-periodic solutions of rectilinear type. [--]
Subject
Publisher
Pleiades Publishing
Published in
Regular and Chaotic Dynamics, 2018, Vol. 23, No. 4, pp. 389–417
Departament
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. InaMat - Institute for Advanced Materials
Publisher version
Sponsorship
The authors have received partial support from Projects MTM 2014-59433-C2-1-P of the
Ministry of Economy and Competitiveness of Spain, from MTM 2017-88137-C2-1-P of the Ministry
of Economy, Industry and Competitiveness of Spain and from the Charles Phelps Taft Foundation.