C. Lemma, Suppose that ? is a rank-two analytic distribution. The sheaf [?, ?] is coherent, contains ? and is everywhere locally generated by three derivations. More precisely, given a point x ? M and two generators X and Y of ? x , the derivations X, Y and

A. Agrachev, A. Barilari, and U. Boscain, Introduction to Riemannian and sub-Riemannian geometry. Monograph
DOI : 10.4171/163-1/1

S. M. Bates and C. G. Moreira, De nouvelles perspectives sur le th??or??me de Morse???Sard, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.1, pp.13-17, 2001.
DOI : 10.1016/S0764-4442(00)01723-7

P. Baum and R. Bott, Singularities of holomorphic foliations, Journal of Differential Geometry, vol.7, issue.3-4, pp.279-342, 1972.
DOI : 10.4310/jdg/1214431158

A. Bella¨?chebella¨?che, The tangent space in sub-Riemannian geometry, pp.1-78, 1996.

E. Bierstone and P. D. Milman, Semianalytic and subanalytic sets. Publications mathématiques de l'I, pp.5-42, 1988.
DOI : 10.1007/bf02699126

URL : http://www.numdam.org/article/PMIHES_1988__67__5_0.pdf

E. Bierstone and P. D. Milman, Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Inventiones Mathematicae, vol.128, issue.2, pp.207-302, 1997.
DOI : 10.1007/s002220050141

E. Bierstone and P. D. Milman, Functoriality in Resolution of Singularities, Publications of the Research Institute for Mathematical Sciences, vol.44, issue.2, pp.609-639, 2008.
DOI : 10.2977/prims/1210167338

H. Hironaka, Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: II, The Annals of Mathematics, vol.79, issue.2, pp.109-203, 1964.
DOI : 10.2307/1970547

H. Hironaka, Introduction to real-analytic sets and real-analytic maps, 1973.

J. Kollár, Lectures on resolution of singularities, Annals of Mathematics Studies, vol.166, 2007.

C. Kottke and R. Melrose, Generalized blow-up of corners and fiber products, Transactions of the American Mathematical Society, vol.367, issue.1, pp.651-705, 2015.
DOI : 10.1090/S0002-9947-2014-06222-3

URL : http://arxiv.org/abs/1107.3320

S. Lojasiewicz, Ensembles semi-analytiques, IHES, 1965.

R. Montgomery, A tour of sub-Riemannian geometries, their geodesics and applications, Mathematical Surveys and Monographs, vol.91, 2002.

R. Narasimhan, Introduction to the theory of analytic spaces. Lect. notes in math, 1966.

D. Panazzolo, Resolution of singularities of real-analytic vector fields in dimension three, Acta Mathematica, vol.197, issue.2, pp.167-289, 2006.
DOI : 10.1007/s11511-006-0011-7

L. Rifford, Sub-Riemannian Geometry and Optimal Transport, Springer Briefs in Mathematics
DOI : 10.1007/978-3-319-04804-8

URL : https://hal.archives-ouvertes.fr/hal-01131787

L. Rifford, Singulì eres minimisantes en géométrie sous-riemannienne [d'après Hakavuori, Séminaire Bourbaki

L. Rifford and E. Trélat, Morse-Sard type results in sub-Riemannian geometry, Mathematische Annalen, vol.6, issue.1, pp.145-159, 2005.
DOI : 10.1007/s00208-004-0622-2

URL : https://hal.archives-ouvertes.fr/hal-00086340

A. Tognoli, Some results in the theory of real analytic spaces, Espaces Analytiques Acad. Roumanie, pp.149-157, 1969.

J. Tougeron, Id??aux de fonctions diff??rentiables. II, Ergebnisse der Mathematik und ihrer Grenzgebiete, 1972.
DOI : 10.5802/aif.341

R. Wheeden and A. Zygmund, Measure and Integral: An Introduction to Real Analysis, 1977.

J. Ww, Resolution of singularities of analytic spaces Proceedings of Gökova Geometry-Topology Conference, Gkova Geometry/Topology Conference (GGT), Gökova, pp.31-63, 2008.

I. Zelenko and M. Zhitomirskii, Rigid paths of generic 2-distributions on 3-manifolds. Duke Math, J, vol.79, issue.2, pp.281-307, 1995.