Numerical methods for sub-Riemannian geometry

Consider a sub-Riemannian geometry (U,Δ,g) where U is a neighborhood of 0 in Rⁿ, Δ⊂TRⁿ a distribution of constant rank m and g a Riemannian metric defined on Δ. One of the main questions related to a given sub-Riemannian structure is the description of the conjugate and cut loci, of the sphere and the wave front. The paper deals with numerical methods, and more precisely it focuses on the numerical computations of the wave front, the sphere and the conjugate points. The algorithms are illustrated on the following sub-Riemannian structures: the Martinet case and the Tangential case (in particular we verify numerically the sub-analyticity of the elliptic sphere and conjecture the non sub-analyticity of the hyperbolic one)