Normalization through invariants in n-dimensional Kepler problems
Fecha
2018Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Impacto
|
10.1134/S1560354718040032
Resumen
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. [--]
Materias
Kepler Hamiltonian in n dimensions,
Perturbed Keplerian problems,
Moser regularization,
Delaunay and Delaunay-like coordinates,
Keplerian invariants,
Periodic and quasi-periodic motions,
KAM theory for properly degenerate Hamiltonians
Editor
Pleiades Publishing
Publicado en
Regular and Chaotic Dynamics, 2018, Vol. 23, No. 4, pp. 389–417
Departamento
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
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.