Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at $0$ in $\R^n,$ $D$ is a rank-2 smooth $(C^\infty $ or $C^\omega )$ distribution and $g$ is a smooth metric on $D$. The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry.
Publié le : 2001-07-05
Classification:
sphere and wave-front with small radii,
abnormal minimizers,
optimal control,
singular trajectories,
sub-Riemannian geometry,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-00086308,
author = {Bonnard, Bernard and Tr\'elat, Emmanuel},
title = {On the role of abnormal minimizers in sub-Riemannian geometry},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00086308}
}
Bonnard, Bernard; Trélat, Emmanuel. On the role of abnormal minimizers in sub-Riemannian geometry. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00086308/