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    Normalization through invariants in n-dimensional Kepler problems

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    Meyer_Normalization.pdf (432.8Kb)
    Date
    2018
    Author
    Meyer, Kenneth Ray 
    Palacián Subiela, Jesús Francisco Upna
    Yanguas Sayas, Patricia Upna
    Version
    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
     
     
     
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    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
    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
     
    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
    https://doi.org/10.1134/S1560354718040032
    URI
    https://hdl.handle.net/2454/29448
    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.
    Appears in Collections
    • Artículos de revista InaMat - InaMat aldizkari artikuluak [147]
    • Artículos de revista - Aldizkari artikuluak [2947]
    • Artículos de revista DEIM - EIMS Aldizkari artikuluak [108]
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