A. A. Agrachev and Y. L. Sachkov, Control theory from the geometric viewpoint, of Encyclopaedia of Mathematical Sciences Control Theory and Optimization, II, 2004.
DOI : 10.1007/978-3-662-06404-7

A. A. Agrachev and A. V. Sarychev, Abnormal sub-Riemannian geodesics: Morse index and rigidity, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.13, issue.6, pp.635-690, 1996.
DOI : 10.1016/S0294-1449(16)30118-4

URL : http://doi.org/10.1016/s0294-1449(16)30118-4

Z. M. Balogh and K. S. Fässler, Rectifiability and Lipschitz extensions into the Heisenberg group, Mathematische Zeitschrift, vol.83, issue.6, pp.673-683, 2009.
DOI : 10.1007/s00209-008-0437-z

Z. M. Balogh, U. Lang, and P. Pansu, Extensions lipschitziennes d???applications entre groupes d???Heisenberg, Annales de l???institut Fourier, vol.66, issue.4, pp.1653-1665, 2016.
DOI : 10.5802/aif.3046

URL : https://hal.archives-ouvertes.fr/hal-01148609

D. Barilari, U. Boscain, and M. Sigalotti, Dynamics, geometry and analysis on sub-Riemannian manifolds, Volumes I-II, EMS Series of Lectures in Mathematics. European Mathematical Society (EMS), 2016.

R. M. Bianchini and G. Stefani, Graded Approximations and Controllability Along a Trajectory, SIAM Journal on Control and Optimization, vol.28, issue.4, pp.903-924, 1990.
DOI : 10.1137/0328050

A. Bonfiglioli, E. Lanconelli, and F. Uguzzoni, Stratified Lie groups and potential theory for their sub- Laplacians, 2007.

Y. Brudnyi and P. Shvartsman, Generalizations of Whitney's extension theorem, Int. Math. Res. Not, issue.3, pp.129-139, 1994.

R. L. Bryant and L. Hsu, Rigidity of integral curves of rank 2 distributions, Inventiones Mathematicae, vol.30, issue.no. 1127, pp.435-461, 1993.
DOI : 10.1007/BF01232676

L. C. Evans and R. F. Gariepy, Measure theory and fine properties of functions, Textbooks in Mathematics, 2015.

C. L. Fefferman, A sharp form of Whitney???s extension theorem, Annals of Mathematics, vol.161, issue.1, pp.509-577, 2005.
DOI : 10.4007/annals.2005.161.509

C. L. Fefferman, A. Israel, and G. K. Luli, Sobolev extension by linear operators, Journal of the American Mathematical Society, vol.27, issue.1, pp.69-145, 2014.
DOI : 10.1090/S0894-0347-2013-00763-8

G. B. Folland and E. M. Stein, Hardy spaces on homogeneous groups, Mathematical Notes, vol.28, 1982.

B. Franchi, R. Serapioni, F. Serra, and . Cassano, Rectifiability and perimeter in the Heisenberg group, Math. Ann, vol.321, issue.3, pp.479-531, 2001.

B. Franchi, R. Serapioni, F. Serra, and . Cassano, On the structure of finite perimeter sets in step 2 Carnot groups, Journal of Geometric Analysis, vol.76, issue.4, pp.421-466, 2003.
DOI : 10.1007/BF02922053

C. Golé and R. Karidi, A note on Carnot geodesics in nilpotent Lie groups, Journal of Dynamical and Control Systems, vol.24, issue.4, pp.535-549, 1995.
DOI : 10.1007/BF02255895

H. Hermes, Control systems which generate decomposable Lie algebras, Journal of Differential Equations, vol.44, issue.2, pp.166-187, 1982.
DOI : 10.1016/0022-0396(82)90012-2

T. Huang and X. Yang, Extremals in some classes of Carnot groups, Science China Mathematics, vol.5, issue.3, pp.633-646, 2012.
DOI : 10.1007/s11425-011-4286-6

B. Kirchheim, F. Serra, and . Cassano, Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.3, issue.54, pp.871-896, 2004.

A. Kozhevnikov, Metric properties of level sets of differentiable maps on Carnot groups, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01178864

E. , L. Donne, A. Ottazzi, and B. Warhurst, Ultrarigid tangents of sub-Riemannian nilpotent groups, Ann. Inst. Fourier (Grenoble), vol.64, issue.6, pp.2265-2282, 2014.

E. , L. Donne, and G. Speight, Lusin approximation for horizontal curves in step 2 Carnot groups, Calc. Var. Partial Differential Equations, vol.55, issue.5, p.111, 2016.

W. Liu and H. J. Sussman, Shortest paths for sub-Riemannian metrics on rank-two distributions, Memoirs of the American Mathematical Society, vol.118, issue.564, p.104, 1995.
DOI : 10.1090/memo/0564

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.2139

N. Lusin, Sur les propriétés des fonctions mesurables, C. R. Acad. Sci, vol.154, pp.1688-1690, 1912.

V. Magnani, TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED??GROUPS, Journal of the Australian Mathematical Society, vol.3, issue.01, pp.76-128, 2013.
DOI : 10.2307/1971484

B. Malgrange, Ideals of differentiable functions. Tata Institute of Fundamental Research Studies in Mathematics, Tata Institute of Fundamental Research, issue.3, 1967.

R. Montgomery, A survey of singular curves in sub-Riemannian geometry, Journal of Dynamical and Control Systems, vol.24, issue.No. 2, pp.49-90, 1995.
DOI : 10.1007/BF02254656

S. Rigot and S. Wenger, Lipschitz Non-extension Theorems into Jet Space Carnot Groups, International Mathematics Research Notices, issue.18, pp.3633-3648, 2010.
DOI : 10.1093/imrn/rnq023

URL : https://hal.archives-ouvertes.fr/hal-00876127

F. and S. Cassano, Some topics of geometric measure theory in Carnot groups In Dynamics, geometry and analysis on sub-Riemannian manifolds, Volume I, EMS Series of Lectures in Mathematics, 2016.

G. Speight, Lusin approximation and horizontal curves in Carnot groups, Revista Matem??tica Iberoamericana, vol.32, issue.4
DOI : 10.4171/RMI/924

H. J. Sussmann, Some properties of vector field systems that are not altered by small perturbations, Journal of Differential Equations, vol.20, issue.2, pp.292-315, 1976.
DOI : 10.1016/0022-0396(76)90109-1

H. J. Sussmann, A General Theorem on Local Controllability, SIAM Journal on Control and Optimization, vol.25, issue.1, pp.158-194, 1987.
DOI : 10.1137/0325011

E. Trélat, Contrôle optimal, Mathématiques Concrètes. [Concrete Mathematics]. Vuibert, Paris, 2005. Théorie & applications. [Theory and applications]

S. K. Vodop-'yanov and I. M. Pupyshev, Whitney-type theorems on the extension of functions on Carnot groups, Sibirsk. Mat. Zh, vol.47, issue.4, pp.731-752, 2006.

S. K. Vodop-'yanov and I. M. Pupyshev, Whitney-type theorems on the extension of functions on the Carnot group, Dokl. Akad. Nauk, vol.406, issue.5, pp.586-590, 2006.

S. Wenger and R. Young, Lipschitz extensions into Jet space Carnot groups, Mathematical Research Letters, vol.17, issue.6, pp.1137-1149, 2010.
DOI : 10.4310/MRL.2010.v17.n6.a12

URL : http://arxiv.org/abs/0911.0919

H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Transactions of the American Mathematical Society, vol.36, issue.1, pp.63-89, 1934.
DOI : 10.1090/S0002-9947-1934-1501735-3

H. Whitney, Differentiable functions defined in closed sets. I, Transactions of the American Mathematical Society, vol.36, issue.2, pp.369-387, 1934.
DOI : 10.1090/S0002-9947-1934-1501749-3

S. Zimmerman, The Whitney extension theorem for C 1 , horizontal curves in H n, J. Geom. Anal

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