This article is cited in 4 papers

Normalization Through Invariants in $n$-dimensional Kepler Problems

Kenneth R. Meyer^a, Jesús F. Palacián^b, Patricia Yanguas<sup>b

a</sup> Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025, USA
^b Departamento de Estadística, Informática y Matemáticas and Institute for Advanced Materials, Universidad Pública de Navarra, 31006 Pamplona, Spain

Abstract: We present a procedure for the normalization of perturbed Keplerian problems in $n$ dimensions based onMoser 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.

Keywords: Kepler Hamiltonian in $n$ dimensions, perturbed Keplerian problems, Moser regularization, Delaunay and Delaunay-like coordinates, Keplerian invariants, regular reduction, periodic and quasi-periodic motions, KAM theory for properly degenerate Hamiltonians.

MSC: 34C20, 34C29, 34C40, 37J40, 70F10, 70K65

Received: 09.01.2018
Accepted: 25.05.2018

Language: English

DOI: 10.1134/S1560354718040032

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