General nilpotent and solvable approximations of almost-Riemannian structures
Yacine Chitour, Université Paris-Saclay, CNRS, CentraleSupélec, , Laboratoire des signaux et systémes, 91190 Gif-sur-Yvette, France, Philippe Jouan, Ronald Manríquez, Lab. R. Salem, CNRS UMR 6085, Université de Rouen, avenue de l'université BP 12, 76801 Saint Étienne-du-Rouvray, France · Discrete and Continuous Dynamical Systems · 2022
It is first shown that the nilpotent or the solvable approximation of an almost-Riemannian structure at a singular point is always a linear almost-Riemannian structure on a Lie group or a homogeneous space.The generic properties of almost-Riemannian structures are then investigated in all dimensions and the generic nilpotent and solvable approximations are identified.