Normalization through invariants in n-dimensional Kepler problems

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 variable...

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Detalles Bibliográficos
Autores: Meyer, Kenneth Ray, Palacián Subiela, Jesús Francisco, Yanguas Sayas, Patricia
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/29448
Acceso en línea:https://hdl.handle.net/2454/29448
Access Level:acceso abierto
Palabra clave: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
Descripción
Sumario: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.