A. Agrachev, Exponential mappings for contact sub-Riemannian structures, Journal of Dynamical and Control Systems, vol.113, issue.3, pp.321-358, 1996.
DOI : 10.1007/BF02269423

A. Agrachev, Geometry of Optimal Control Problems and Hamiltonian Systems, In Nonlinear and optimal control theory Lecture Notes in Math, pp.1-59, 1932.
DOI : 10.1007/978-3-540-77653-6_1

A. Agrachev, Any sub-Riemannian metric has points of smoothness, Doklady Mathematics, vol.79, issue.1, pp.295-298, 2009.
DOI : 10.1134/S106456240901013X

A. Agrachev and D. Barilari, Sub-Riemannian structures on 3D lie groups, Journal of Dynamical and Control Systems, vol.45, issue.2, pp.21-44, 2012.
DOI : 10.1007/s10883-012-9133-8

URL : https://hal.archives-ouvertes.fr/hal-00672261

A. Agrachev, D. Barilari, and U. Boscain, Introduction to Riemannian and sub-Riemannian geometry (Lecture Notes)

A. Agrachev, D. Barilari, and U. Boscain, On the Hausdorff volume in sub-Riemannian geometry. Calc. Var. and PDE's, pp.3-4355, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00672260

A. Agrachev, D. Barilari, P. W. Lee, and L. Rizzi, Curvature for contact sub-Riemannian manifolds, 2014.

A. Agrachev, D. Barilari, and L. Rizzi, Curvature, 2013.
DOI : 10.1007/978-3-662-06404-7_23

URL : https://hal.archives-ouvertes.fr/hal-00838195

A. Agrachev, U. Boscain, J. Gauthier, and F. Rossi, The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups, Journal of Functional Analysis, vol.256, issue.8, pp.2621-2655, 2009.
DOI : 10.1016/j.jfa.2009.01.006

A. Agrachev and R. Gamkrelidze, Symplectic methods for optimization and control. In Geometry of feedback and optimal control, Monogr. Textbooks Pure Appl. Math, vol.207, pp.19-77, 1998.

A. Agrachev, R. V. Gamkrelidze, and A. V. Sarychev, Local invariants of smooth control systems, Acta Applicandae Mathematicae, vol.16, issue.155, pp.191-237, 1989.
DOI : 10.1007/BF01307214

A. Agrachev and J. Gauthier, On the subanalyticity of Carnot???Caratheodory distances, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.18, issue.3, pp.359-382, 2001.
DOI : 10.1016/S0294-1449(00)00064-0

A. Agrachev, L. Rizzi, and P. Silveira, On conjugate times of LQ optimal control problems. ArXiv e-prints, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01096715

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. Agrachev and I. Zelenko, Geometry of Jacobi curves. I, Journal of Dynamical and Control Systems, vol.8, issue.1, pp.93-140, 2002.
DOI : 10.1023/A:1013904801414

A. A. Agrachev and R. V. Gamkrelidze, Feedback-invariant optimal control theory and differential geometry???I. Regular extremals, Journal of Dynamical and Control Systems, vol.29, issue.3, pp.343-389, 1997.
DOI : 10.1007/BF02463256

A. A. Agrachev and P. Lee, Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds, Mathematische Annalen, vol.259, issue.1, 2009.
DOI : 10.1007/s00208-014-1034-6

L. Ambrosio, N. Gigli, and G. Savaré, Metric measure spaces with Riemannian Ricci curvature bounded from below, Duke Mathematical Journal, vol.163, issue.7, 2011.
DOI : 10.1215/00127094-2681605

URL : https://hal.archives-ouvertes.fr/hal-00769376

D. Barilari, Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry, Journal of Mathematical Sciences, vol.136, issue.2, 2011.
DOI : 10.1007/s10958-013-1585-1

URL : https://hal.archives-ouvertes.fr/hal-00672262

D. Barilari, U. Boscain, G. Charlot, and R. W. Neel, On the heat diffusion for generic Riemannian and sub-Riemannian structures. ArXiv e-prints, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00879444

D. Barilari, U. Boscain, and J. Gauthier, On 2-Step, Corank 2, Nilpotent Sub-Riemannian Metrics, SIAM Journal on Control and Optimization, vol.50, issue.1, pp.559-582, 2012.
DOI : 10.1137/110835700

URL : https://hal.archives-ouvertes.fr/hal-00596665

D. Barilari, U. Boscain, and R. W. Neel, Small-time heat kernel asymptotics at the sub-Riemannian cut locus, Journal of Differential Geometry, vol.92, issue.3, pp.373-416, 2012.
DOI : 10.4310/jdg/1354110195

URL : https://hal.archives-ouvertes.fr/hal-00687651

D. Barilari and A. Lerario, Geometry of Maslov cycles In Geometric Control Theory and sub-Riemannian Geometry, INdAM Series 5, 2013.

D. Barilari and L. Rizzi, A formula for Popp's volume in sub-Riemannian geometry. Analysis and Geometry in Metric Spaces, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00751222

F. Baudoin, M. Bonnefont, and N. Garofalo, A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincar?? inequality, Mathematische Annalen, vol.28, issue.1, pp.1-28, 2013.
DOI : 10.1007/s00208-013-0961-y

F. Baudoin, M. Bonnefont, N. Garofalo, and I. H. Munive, Volume and distance comparison theorems for sub-Riemannian manifolds. ArXiv e-prints, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00779393

F. Baudoin and N. Garofalo, Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries, Journal of the European Mathematical Society, vol.19, issue.1, 2011.
DOI : 10.4171/JEMS/663

F. Baudoin and J. Wang, Curvature Dimension Inequalities and Subelliptic Heat Kernel Gradient Bounds on Contact Manifolds, Potential Analysis, vol.314, issue.1, 2013.
DOI : 10.1007/s11118-013-9345-x

A. Bellaïche, The tangent space in sub-Riemannian geometry, Sub-Riemannian geometry, pp.1-78, 1996.

U. Boscain and J. Gauthier, On the Spherical Hausdorff Measure in Step 2 Corank 2 Sub-Riemannian Geometry, SIAM Journal on Control and Optimization, vol.51, issue.6, 2012.
DOI : 10.1137/12089449X

URL : https://hal.archives-ouvertes.fr/hal-00739965

U. Boscain and C. Laurent, L???op??rateur de Laplace-Beltrami en G??om??trie presque-Riemannienne, Annales de l???institut Fourier, vol.63, issue.5, 2011.
DOI : 10.5802/aif.2813

U. Boscain and F. Rossi, Invariant Carnot???Caratheodory Metrics on $S^3$, $SO(3)$, $SL(2)$, and Lens Spaces, SL(2), and lens spaces, pp.1851-1878, 2008.
DOI : 10.1137/070703727

R. W. Brockett, Control Theory and Singular Riemannian Geometry, New directions in applied mathematics, pp.11-27, 1980.
DOI : 10.1007/978-1-4612-5651-9_2

R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths, Exterior differential systems, of Mathematical Sciences Research Institute Publications, 1991.
DOI : 10.1007/978-1-4613-9714-4

J. Coron, Control and nonlinearity, volume 136 of Mathematical Surveys and Monographs, 2007.

L. E. Fa?-ibusovich, Existence and uniqueness of extremal solutions of the Riccati equation and symplectic geometry, Funktsional. Anal. i Prilozhen, vol.19, issue.1, pp.85-86, 1985.

T. Gallouët, Transport optimal : régularité et applications, These, Ecole normale supérieure de lyon -ENS LYON, 2012.

V. Gershkovich and A. Vershik, Nonholonomic manifolds and nilpotent analysis, Journal of Geometry and Physics, vol.5, issue.3, pp.407-452, 1988.
DOI : 10.1016/0393-0440(88)90032-0

R. Ghezzi and F. Jean, A new class of (H k , 1)-rectifiable subsets of metric spaces. ArXiv preprint, arXiv:1109, p.3181, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00623647

M. Gromov, Carnot-Carathéodory spaces seen from within In Sub-Riemannian geometry, Progr. Math, vol.144, pp.79-323, 1996.

F. Jean, Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning
DOI : 10.1007/978-3-319-08690-3

URL : https://hal.archives-ouvertes.fr/hal-01137580

N. Juillet, Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group, International Mathematics Research Notices, issue.13, pp.2347-2373, 2009.
DOI : 10.1093/imrn/rnp019

V. Jurdjevic, Geometric control theory, volume 52 of Cambridge Studies in Advanced Mathematics, 1997.

T. Kato, Perturbation theory for linear operators, Classics in Mathematics, 1995.

P. W. Lee, C. Li, and I. Zelenko, Measure contraction properties of contact sub- Riemannian manifolds with symmetry. ArXiv e-prints, 2013.

C. Li and I. Zelenko, Jacobi equations and Comparison Theorems for corank 1 sub-Riemannian structures with symmetries, Journal of Geometry and Physics, vol.61, issue.4, pp.781-807, 2011.
DOI : 10.1016/j.geomphys.2010.12.009

G. Loeper, On the regularity of solutions of optimal transportation problems, Acta Mathematica, vol.202, issue.2, pp.241-283, 2009.
DOI : 10.1007/s11511-009-0037-8

J. Lott and C. Villani, Ricci curvature for metric-measure spaces via optimal transport, Annals of Mathematics, vol.169, issue.3, pp.903-991, 2009.
DOI : 10.4007/annals.2009.169.903

K. R. Meyer and G. R. Hall, Introduction to Hamiltonian dynamical systems and the N body problem, Applied Mathematical Sciences, vol.90, 1992.
DOI : 10.1007/978-1-4757-4073-8

J. W. Milnor, Topology from the differentiable viewpoint Princeton Landmarks in Mathematics, 1997.

J. Mitchell, On Carnot-Carath??odory metrics, Journal of Differential Geometry, vol.21, issue.1, pp.35-45, 1985.
DOI : 10.4310/jdg/1214439462

I. Moiseev and Y. L. Sachkov, Maxwell strata in sub-Riemannian problem on the group of motions of a plane, ESAIM: Control, Optimisation and Calculus of Variations, vol.16, issue.2, pp.380-399, 2010.
DOI : 10.1051/cocv/2009004

R. Montgomery, A tour of subriemannian geometries, their geodesics and applications, volume 91 of Mathematical Surveys and Monographs, 2002.

S. B. Myers, Riemannian manifolds with positive mean curvature. Duke Math, J, vol.8, pp.401-404, 1941.
DOI : 10.1215/s0012-7094-41-00832-3

S. Ohta, Abstract, Analysis and Geometry in Metric Spaces, vol.2, issue.1, 2013.
DOI : 10.2478/agms-2014-0003

S. Ohta, On the curvature and heat flow on Hamiltonian systems. ArXiv e-prints, 2013.

S. Ohta and K. Sturm, Bochner???Weitzenb??ck formula and Li???Yau estimates on Finsler manifolds, Advances in Mathematics, vol.252, pp.429-448, 2014.
DOI : 10.1016/j.aim.2013.10.018

L. S. Pontryagin, V. G. Boltyanski?-i, R. V. Gamkrelidze, and E. F. Mishchenko, Selected works Classics of Soviet Mathematics. Gordon & Breach Science Publishers The mathematical theory of optimal processes, Edited and with a preface by R. V. Gamkrelidze, Translated from the Russian by, 1986.

B. Riemann, Über die hypothesen, welche der geometrie zu grunde liegen. Göttengen, p.1854

L. Rifford, Sub-Riemannian Geometry and Optimal Transport, Lecture Notes, vol.146, 2012.
DOI : 10.1007/978-3-319-04804-8

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

L. Rifford, Ricci curvatures in Carnot groups, Mathematical Control and Related Fields, vol.3, issue.4, pp.467-487, 2013.
DOI : 10.3934/mcrf.2013.3.467

Y. L. Sachkov, Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane, ESAIM: Control, Optimisation and Calculus of Variations, vol.16, issue.4, pp.1018-1039, 2010.
DOI : 10.1051/cocv/2009031

R. S. Strichartz, Sub-Riemannian geometry, Journal of Differential Geometry, vol.24, issue.2, pp.221-263, 1986.
DOI : 10.4310/jdg/1214440436

K. Sturm, On the geometry of metric measure spaces, Acta Mathematica, vol.196, issue.1, pp.65-131, 2006.
DOI : 10.1007/s11511-006-0002-8

K. Sturm, On the geometry of metric measure spaces, Acta Mathematica, vol.196, issue.1, pp.133-177, 2006.
DOI : 10.1007/s11511-006-0002-8

C. Villani, Optimal transport, 2009.
DOI : 10.1007/978-3-540-71050-9

URL : https://hal.archives-ouvertes.fr/hal-00974787

B. Y. Wu and Y. L. Xin, Comparison theorems in Finsler geometry and their applications, Mathematische Annalen, vol.54, issue.2B, pp.177-196, 2007.
DOI : 10.1007/s00208-006-0031-9

I. Zelenko and C. Li, Differential geometry of curves in Lagrange Grassmannians with given Young diagram, Differential Geometry and its Applications, vol.27, issue.6, pp.723-742, 2009.
DOI : 10.1016/j.difgeo.2009.07.002