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 |
Acceso al artículo completo |