no. 6
Optimal control/Differential geometry
Generic singularities of the 3D-contact sub-Riemannian conjugate locus
[Singularités génériques du lieu conjugé en géométrie sous-riemannienne dans le cas 3D-contact]

Présenté par : Jean-Michel Coron

Bonnet, Benoît1 ; Gauthier, Jean-Paul1 ; Rossi, Francesco2
1 Aix Marseille Université, CNRS, ENSAM, Université de Toulon, LIS, Marseille, France
2 Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Padova, Italy
Comptes Rendus. Mathématique, Tome 357 (2019) no. 6, pp. 520-527.

Dans cet article, nous étendons et achevons la classification des singularités génériques du lieu conjugué sous-riemannien 3D-contact au voisinage de l'origine.

In this paper, we extend and complete the classification of the generic singularities of the 3D-contact sub-Riemmanian conjugate locus in a neighborhood of the origin.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.05.008
Bonnet, Benoît 1 ; Gauthier, Jean-Paul 1 ; Rossi, Francesco 2

1 Aix Marseille Université, CNRS, ENSAM, Université de Toulon, LIS, Marseille, France
2 Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Padova, Italy 
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Bonnet, Benoît; Gauthier, Jean-Paul; Rossi, Francesco. Generic singularities of the 3D-contact sub-Riemannian conjugate locus. Comptes Rendus. Mathématique, Tome 357 (2019) no. 6, pp. 520-527. doi : 10.1016/j.crma.2019.05.008. http://www.numdam.org/articles/10.1016/j.crma.2019.05.008/

[1] Agrachev, A. Methods of control theory in nonholonomic geometry, Proc. ICM-94, Birkhäuser, Zürich, Switzerland, 1995

[2] Agrachev, A. Exponential mappings for contact sub-Riemannian structures, J. Dyn. Control Syst., Volume 2 (1996) no. 3, pp. 321-358

[3] Agrachev, A.; Chakir, H.; Gauthier, J.-P. Subriemannian metrics on R3, Proc. Can. Math. Soc., Volume 25 (1998), pp. 29-76

[4] Agrachev, A.; Charlot, G.; Gauthier, J.-P.; Zakalyukin, V. On subriemannian caustics and wave fronts for contact distributions in the three space, J. Dyn. Control Syst., Volume 6 (2000) no. 3, pp. 365-395

[5] Agrachev, A.; Barilari, D.; Boscain, U. A Comprehensive Introduction to Sub-Riemannian Geometry, Cambridge Studies in Advanced Mathematics, 2019

[6] Chakir, H.; Gauthier, J.-P.; Kupka, I. Small sub-Riemannian balls on R3, J. Dyn. Control Syst., Volume 2 (1996) no. 3, pp. 359-421

[7] Hirsch, M.W. Differential Topology, Springer Graduate Texts in Mathematics, vol. 33, 1974

[8] Sacchelli, L. Short geodesics losing optimality in contact sub-Riemannian manifolds and stability of the 5-dimensional caustic, SIAM J. Control Optim. (2019) (accepted for publication in) | arXiv

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