Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature.

Título inglés Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature.
Título español Sistemas hamiltonianos no singulares y flujos geodésicos sobre superficies con curvatura negativa.
Autor/es Lacomba, Ernesto A. ; Reyes, J. Guadalupe
Organización Dep. Mat. Univ. Autón. Metropolitana-Iztapalapa, México D.F., Méjico
Revista 0214-1493
Publicación 1998, 42 (2): 267-299, 15 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés We extend here results for escapes in any given direction of the configuration space of a mechanical system with a non singular bounded at infinity homogeneus potential of degree -1, when the energy is positive. We use geometrical methods for analyzing the parallel and asymptotic escapes of this type of systems. By using Riemannian geometry methods we prove under suitable conditions on the potential that all the orbits escaping in a given direction are asymptotically parallel among themselves. We introduce a conformal Riemannian metric with negative curvature in the interior of the Hill's region for a fixed positive energy level and we consider the boundary as a singular part of the infinity. The associated geodesic flow has as solution curves those of the problem for a fixed energy. We perform the compactification of the region via the limiting directions of the geodesic flow, obtaining a closed unit disk with a quasi-complete metric of negative curvature.
Clasificación UNESCO 221203 ; 120411
Palabras clave español Sistema hamiltoniano ; Flujos geodésicos ; Sistemas mecánicos ; Curvatura ; Ecuaciones diferenciales ; Teoría del potencial ; Comportamiento asintótico ; Conservación de la energía ; Métricas riemannianas ; Problema de Hill
Código MathReviews MR1676028
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