Articles en préparation/Works in progress:
L. Rifford, Nonholonomic Variations: An Introduction to Sub-Riemannian Geometry.
A. Figalli, L. Rifford, C. Villani, Continuity of optimal transport on Riemannian manifolds in presence of focalization.
A. Figalli, L. Rifford, Closing Aubry sets II.
A. Figalli, L. Rifford, Closing Aubry sets I, 61 pages. pdf
A. Figalli, L. Rifford, C. Villani, Nearly round spheres look convex, 34 pages. pdf
M. Castelpietra, L. Rifford, Regularity properties of the distance function to conjugate and cut loci for viscosity solutions of Hamilton-Jacobi equations and applications in Riemannian geometry, ESAIM Control Optim. Calc. Var., 24 pages, à paraître/to appear. pdf
A. Figalli, L. Rifford, Mass Transportation on sub-Riemannian Manifolds, Geom. Funct. Anal., 46 pages, à paraître/to appear. pdf
L. Rifford, E. Trélat, On the stabilization problem for nonholonomic distributions, J. Eur. Math. Soc., 11(2):223-255, 2009. pdf
A. Fathi, A. Figalli, L. Rifford, On the Hausdorff Dimension of the Mather Quotient, Comm. Pure Appl. Math., 62(4):445-500, 2009. pdf
P. Cannarsa, L. Rifford, Semiconcavity results for optimal control problems admitting no singular minimizing controls, Ann. Inst. H. Poincaré Anal. Non Linéaire, 25(4):773-802, 2008. pdf
L. Rifford, On viscosity
solutions of certain Hamilton-Jacobi equations: Regularity results and
generalized Sard's Theorems, Comm.
Partial Differential Equations, 33(3):517-559, 2008. pdf
L. Rifford, A refinement of the Benoist Theorem on the size of Dini subdifferentials, Commun. Pure Appl. Anal., 7(1):119-124, 2008. pdf
L. Rifford, À propos des sphères sous-riemanniennes, Bull. Belg. Math. Soc. Simon Stevin, 13(3):521-526, 2006. pdf
M.-O. Czarnecki, L. Rifford, Approximation and regularization of Lipschitz functions : convergence of the gradients, Trans. Amer. Math. Soc., 358(10):4467-4520, 2006.
L. Rifford, On the existence of local smooth repulsive stabilizing feedbacks in dimension three, J. Differential Equations, 226(2):429-500, 2006. pdf
L. Rifford, E. Trélat, Morse-Sard type results in sub-Riemannian geometry, Math. Ann., 332(1):145-159, 2005. pdf
L. Rifford, Stratified semiconcave control-Lyapunov functions and the stabilization problem, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22(3):343-384, 2005. pdf
L. Rifford, A Morse-Sard theorem for the distance function on Riemannian manifolds, Manuscripta Math., 113:251-265, 2004. pdf
M. Malisoff, L. Rifford, E. D. Sontag, Asymptotic controllability implies input to state stability, SIAM J. Control Optim., 42(6):2221-2238, 2004. pdf
L. Rifford, Singularities of viscosity solutions and the stabilization problem in the plane, Indiana Univ. Math. J, 52(5):1373-1396, 2003. pdf
L. Rifford, Range of the gradient of a smooth bump function in finite dimensions, Proc. Amer. Math. Soc., 131(10):3063-3066, 2003. pdf
L. Rifford, Semiconcave control-Lyapunov functions and stabilizing feedbacks, SIAM J. Control Optim., 41(3):659-681, 2002.
F. H. Clarke, L. Rifford, R. J. Stern, Feedback in state constrained optimal control, ESAIM Control Optim. Calc. Var., 7:97-133, 2002.
L. Rifford, On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients, ESAIM Control Optim. Calc. Var., 6:593-611, 2001. pdf
L. Rifford, Existence of Lipschitz and semiconcave control-Lyapunov functions, SIAM J. Control Optim., 39(4):1043-1064, 2000. pdf
F. H. Clarke, Yu. S. Ledyaev, L. Rifford, R. J. Stern, Feedback stabilization and Lyapunov functions, SIAM J. Control Optim., 39(1):25-48, 2000. pdf
Actes de colloques/Proceedings:
L. Rifford, Stabilization problem for nonholonomic control systems, in Geometric Control and Nonsmooth Analysis, Series on Advances in Mathematics for Applied Sciences Vol. 76, World Scientific, pp. 260-269, 2008. pdf
L. Rifford, The stabilization problem on surfaces, Rend. Semin. Mat. Torino, Control Theory and Stabilization II, 64(1):55-61, 2006. pdf
L. Rifford, The stabilization problem: AGAS and SRS feedbacks, in Optimal Control, Stabilization, and Nonsmooth Analysis, Lectures Notes in Control and Information Sciences Vol. 301, Springer-Verlag, Heidelberg, 2004, pp. 173-184. pdf
M. Malisoff, L. Rifford, E. D. Sontag, Remark on input to state stabilization, in Proceedings of the 42nd IEEE Conference on Decision and Control (Maui, HI, December 2003),pp. 1053-1058. pdf
Exposés/Talks:
Optimal Transportation on Sub-Riemannian Manifolds, in Optimal Transportations and Applications, SNS Pisa (Italy), 2008. pdf
Optimal Transportation on Sub-Riemannian Manifolds, in 50 Years of Optimal Control, Banach Center, Bedlewo (Poland), 2008. pdf
On the Mather Quotient, in Atelier sur les aspects de la mécanique céleste, Institut Henri Poincaré, Paris, 2007. pdf
Thèse
de doctorat/PhD Thesis:
Problèmes de stabilisation en théorie du contrôle. Thèse soutenue le 11 mai 2000 à l'Université Claude Bernard Lyon I, Mention très honorable avec félicitations. Jury : H. Attouch (président), J.-B. Hiriart-Urruty, E.D. Sontag, R. Vinter (rapporteurs), J.-B. Baillon, J. Blum, F. Clarke, J.-M. Coron (examinateurs). pdf
Habilitation à diriger des recherches/HDR Thesis:
Problème de Stabilisation et Géométrie Sous-Riemannienne. Soutenue le 24 octobre 2005 à l'Université de Paris-Sud. Jury : H. Attouch (président), B. Bonnard, A. Bressan, J.-M. Coron (rapporteurs), F. Clarke, A. Fathi, P. Pansu (examinateurs). pdf