On the Canonical Treatment of Gylden–Type Problems Based on Quasi–Keplerian Systems

Luis Floría ^[1]
1. [1] Universidad de Zaragoza
  
  Universidad de Zaragoza
  
  Zaragoza, España
Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals, Anastasio Pedro Santos Yanguas, 2001, ISBN 8469961446, págs. 519-520
Idioma: inglés
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Resumen
- We study the performance of some mappings (generalized Delaunay-like transformations and torsions, in the 6-dimensional phase space; TR-like maps, in the extended phase space), when applied to perturbed two-body problems with a time-varying Keplerian parameter μ(t), i.e., to Gylden-type systems. Time- dependent perturbations based on quasi-Keplerian systems are considered. We introduce appropriate canonical variables, parallelling the Delaunay elements and the Delaunay-Similar variables of Scheifele, in terms of which our perturbed Gylden systems can be brought into the form of perturbed Kepler problems.