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

Ernesto A. Lacomba; J. Guadalupe Reyes

Publicacions Matemàtiques (1998)

- Volume: 42, Issue: 2, page 267-299
- ISSN: 0214-1493

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topLacomba, Ernesto A., and Reyes, J. Guadalupe. "Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature.." Publicacions Matemàtiques 42.2 (1998): 267-299. <http://eudml.org/doc/41355>.

@article{Lacomba1998,

abstract = {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.},

author = {Lacomba, Ernesto A., Reyes, J. Guadalupe},

journal = {Publicacions Matemàtiques},

keywords = {Sistema hamiltoniano; Flujos geodésicos; Sistemas mecánicos; Curvatura; Ecuaciones diferenciales; Teoría del potencial; Comportamiento asintótico; Conservación de la energía; Métricas riemannianas; Problema de Hill; geodesic flow; Hamiltonian system; negative curvature; Lagrangian; conformal metric},

language = {eng},

number = {2},

pages = {267-299},

title = {Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature.},

url = {http://eudml.org/doc/41355},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Lacomba, Ernesto A.

AU - Reyes, J. Guadalupe

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

JO - Publicacions Matemàtiques

PY - 1998

VL - 42

IS - 2

SP - 267

EP - 299

AB - 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.

LA - eng

KW - Sistema hamiltoniano; Flujos geodésicos; Sistemas mecánicos; Curvatura; Ecuaciones diferenciales; Teoría del potencial; Comportamiento asintótico; Conservación de la energía; Métricas riemannianas; Problema de Hill; geodesic flow; Hamiltonian system; negative curvature; Lagrangian; conformal metric

UR - http://eudml.org/doc/41355

ER -

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