Propriétés génériques des trajectoires singulières

Yacine Chitour; Frédéric Jean; Emmanuel Trélat

doi:10.1016/S1631-073X(03)00252-8

Propriétés génériques des trajectoires singulières

Yacine Chitour
, Frédéric Jean
, Emmanuel Trélat

Université Paris-Saclay

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

17 Citations (Scopus)

Résumé

We give genericity results for singular trajectories in sub-Riemannian geometry: generically (in the sense of the Whitney topology), every singular trajectory is of minimal order and of corank 1 and in particular is not of Goh type if the rank of the distribution is greater or equal to 3. We extend these results to control-affine systems.

Titre traduit de la contribution	Generic properties of singular trajectories
langue originale	Français
Pages (de - à)	49-52
Nombre de pages	4
journal	Comptes Rendus Mathematique
Volume	337
Numéro de publication	1
Les DOIs	https://doi.org/10.1016/S1631-073X(03)00252-8
état	Publié - 1 juil. 2003

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10.1016/S1631-073X(03)00252-8

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title = "Propri{\'e}t{\'e}s g{\'e}n{\'e}riques des trajectoires singuli{\`e}res",

abstract = "We give genericity results for singular trajectories in sub-Riemannian geometry: generically (in the sense of the Whitney topology), every singular trajectory is of minimal order and of corank 1 and in particular is not of Goh type if the rank of the distribution is greater or equal to 3. We extend these results to control-affine systems.",

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AU - Jean, Frédéric

AU - Trélat, Emmanuel

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N2 - We give genericity results for singular trajectories in sub-Riemannian geometry: generically (in the sense of the Whitney topology), every singular trajectory is of minimal order and of corank 1 and in particular is not of Goh type if the rank of the distribution is greater or equal to 3. We extend these results to control-affine systems.

AB - We give genericity results for singular trajectories in sub-Riemannian geometry: generically (in the sense of the Whitney topology), every singular trajectory is of minimal order and of corank 1 and in particular is not of Goh type if the rank of the distribution is greater or equal to 3. We extend these results to control-affine systems.

U2 - 10.1016/S1631-073X(03)00252-8

DO - 10.1016/S1631-073X(03)00252-8

M3 - Article

AN - SCOPUS:0042205053

SN - 1631-073X

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EP - 52

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

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ER -

Propriétés génériques des trajectoires singulières

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