6533b85cfe1ef96bd12bc890

RESEARCH PRODUCT

Singular systems in dimension 3: Cuspidal case and tangent elliptic flat case

Michèle Pelletier

subject

Dimension (vector space)Homogeneous spaceMathematical analysisTangentTangent vectorAffine transformationExceptional divisorSingular controlEigenvalues and eigenvectorsMathematics

description

We study two singular systems in R3. The first one is affine in control and we achieve weighted blowings-up to prove that singular trajectories exist and that they are not locally time optimal. The second one is linear in control. The characteristic vector field in sub-Riemannian geometry is generically singular at isolated points in dimension 3. We define a case with symmetries, which we call flat, and we parametrize the sub-Riemannian sphere. This sphere is subanalytic.

yearjournalcountryeditionlanguage
2007-10-02
https://doi.org/10.1007/bfb0110302