Propriétés génériques des trajectoires singulières

Yacine Chitour; Frédéric Jean; Emmanuel Trélat

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

Propriétés génériques des trajectoires singulières

Translated title of the contribution: Generic properties of singular trajectories

Yacine Chitour
, Frédéric Jean
, Emmanuel Trélat

Université Paris-Saclay

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

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.

Translated title of the contribution	Generic properties of singular trajectories
Original language	French
Pages (from-to)	49-52
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	337
Issue number	1
DOIs	https://doi.org/10.1016/S1631-073X(03)00252-8
Publication status	Published - 1 Jul 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.",

author = "Yacine Chitour and Fr{\'e}d{\'e}ric Jean and Emmanuel Tr{\'e}lat",

year = "2003",

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AU - Chitour, Yacine

AU - Jean, Frédéric

AU - Trélat, Emmanuel

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Y1 - 2003/7/1

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

VL - 337

SP - 49

EP - 52

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 1

ER -

Propriétés génériques des trajectoires singulières

Abstract

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