On almost-Riemannian surfaces
- [1] Department of Mathematical Sciences and Centre of Computational and Integrative Biology, Rutgers University Camden - Camden, 311 N 5th Street, Camden, NJ 08102, USA.
Séminaire de théorie spectrale et géométrie (2010-2011)
- Volume: 29, page 15-49
- ISSN: 1624-5458
Access Full Article
topAbstract
topHow to cite
topReferences
top- A. Agrachev, Compactness for sub-Riemannian length-minimizers and subanalyticity, Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), 1-12 (2001) Zbl1039.53038MR1845741
- A. Agrachev, B. Bonnard, M. Chyba, I. Kupka, Sub-Riemannian sphere in Martinet flat case, ESAIM Control Optim. Calc. Var. 2 (1997), 377-448 Zbl0902.53033MR1483765
- A. A. Agrachev, A “Gauss-Bonnet formula” for contact sub-Riemannian manifolds, Dokl. Akad. Nauk 381 (2001), 583-585 Zbl1044.53021MR1890409
- A. A. Agrachev, D. Barilari, U. Boscain, Introduction to Riemannian and sub-Riemannian geometry (Lecture Notes) Zbl1236.53030
- A. A. Agrachev, U. Boscain, G. Charlot, R. Ghezzi, M. Sigalotti, Two-Dimensional Almost-Riemannian Structures With Tangency Points, Proceedings of the 48th IEEE Conference on Decision and Control, December 16-18, 2009. Shangai, China. Zbl1192.53029MR2629880
- A. A. Agrachev, U. Boscain, G. Charlot, R. Ghezzi, M. Sigalotti, Two-dimensional almost-Riemannian structures with tangency points, Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), 793-807 Zbl1192.53029MR2629880
- Andrei Agrachev, Ugo Boscain, Mario Sigalotti, A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds, Discrete Contin. Dyn. Syst. 20 (2008), 801-822 Zbl1198.49041MR2379474
- Andrei Agrachev, Igor Zelenko, On feedback classification of control-affine systems with one- and two-dimensional inputs, SIAM J. Control Optim. 46 (2007), 1431-1460 (electronic) Zbl1140.93018MR2346387
- Andrei A. Agrachev, Yuri L. Sachkov, Control theory from the geometric viewpoint, 87 (2004), Springer-Verlag, Berlin Zbl1062.93001MR2062547
- André Bellaïche, The tangent space in sub-Riemannian geometry, Sub-Riemannian geometry 144 (1996), 1-78, Birkhäuser, Basel Zbl0862.53031MR1421822
- B. Bonnard, J.-B. Caillau, R. Sinclair, M. Tanaka, Conjugate and cut loci of a two-sphere of revolution with application to optimal control, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), 1081-1098 Zbl1184.53036MR2542715
- Bernard Bonnard, Jean Baptiste Caillau, Singular Metrics on the Two-Sphere in Space Mechanics Zbl1127.49017
- Bernard Bonnard, Grégoire Charlot, Roberta Ghezzi, Gabriel Janin, The Sphere and the Cut Locus at a Tangency Point in Two-Dimensional Almost-Riemannian Geometry, J. Dynam. Control Systems 17 (2011), 141-161 Zbl1209.53014MR2765542
- Bernard Bonnard, Monique Chyba, Méthodes géométriques et analytiques pour étudier l’application exponentielle, la sphère et le front d’onde en géométrie sous-riemannienne dans le cas Martinet, ESAIM Control Optim. Calc. Var. 4 (1999), 245-334 (electronic) Zbl0929.53016MR1696290
- U. Boscain, G. Charlot, R. Ghezzi, M. Sigalotti, Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces, Journal of Geometric Analysis, 1-18 Zbl1259.53031
- Ugo Boscain, Thomas Chambrion, Grégoire Charlot, Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy, Discrete Contin. Dyn. Syst. Ser. B 5 (2005), 957-990 Zbl1084.81083MR2170218
- Ugo Boscain, G. Charlot, R. Ghezzi, Normal forms and invariants for 2-dimensional almost-Riemannian structures Zbl1260.53063
- Ugo Boscain, Grégoire Charlot, Resonance of minimizers for -level quantum systems with an arbitrary cost, ESAIM Control Optim. Calc. Var. 10 (2004), 593-614 (electronic) Zbl1072.49002MR2111082
- Ugo Boscain, Grégoire Charlot, Jean-Paul Gauthier, Stéphane Guérin, Hans-Rudolf Jauslin, Optimal control in laser-induced population transfer for two- and three-level quantum systems, J. Math. Phys. 43 (2002), 2107-2132 Zbl1059.81195MR1893663
- Ugo Boscain, Camille Laurent, The Laplace–Beltrami operator in almost-Riemannian Geometry Zbl1314.58017
- Ugo Boscain, Mario Sigalotti, High-order angles in almost-Riemannian geometry, Actes de Séminaire de Théorie Spectrale et Géométrie. Vol. 24. Année 2005–2006 25 (2008), 41-54, Univ. Grenoble I Zbl1159.53320MR2478807
- Bruno Franchi, Ermanno Lanconelli, Une métrique associée à une classe d’opérateurs elliptiques dégénérés, Rend. Sem. Mat. Univ. Politec. Torino (1983), 105-114 (1984) Zbl0553.35033MR745979
- V. V. Grušin, A certain class of hypoelliptic operators, Mat. Sb. (N.S.) 83 (125) (1970), 456-473 MR279436
- Morris W. Hirsch, Differential topology, 33 (1994), Springer-Verlag, New York Zbl0356.57001MR1336822
- Frédéric Jean, Uniform estimation of sub-Riemannian balls, J. Dynam. Control Systems 7 (2001), 473-500 Zbl1029.53039MR1854033
- Ravindra Shripad Kulkarni, Curvature and metric, Ann. of Math. (2) 91 (1970), 311-331 Zbl0191.19903MR257932
- Fernand Pelletier, Quelques propriétés géométriques des variétés pseudo-riemanniennes singulières, Ann. Fac. Sci. Toulouse Math. (6) 4 (1995), 87-199 Zbl0845.53044MR1344719
- Fernand Pelletier, Liane Valère Bouche, The problem of geodesics, intrinsic derivation and the use of control theory in singular sub-Riemannian geometry, Actes de la Table Ronde de Géométrie Différentielle (Luminy, 1992) 1 (1996), 453-512, Soc. Math. France, Paris Zbl0877.53029MR1427768
- L. S. Pontryagin, V. G. Boltyanskiĭ, R. V. Gamkrelidze, E. F. Mishchenko, The Mathematical Theory of Optimal Processes, (1983), “Nauka”, Moscow Zbl0516.49001MR719372
- Marilena Vendittelli, Giuseppe Oriolo, Frédéric Jean, Jean-Paul Laumond, Nonhomogeneous nilpotent approximations for nonholonomic systems with singularities, IEEE Trans. Automat. Control 49 (2004), 261-266 MR2034349