Comptes Rendus
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

Benoît Bonnet1 ; Jean-Paul Gauthier1 ; Francesco Rossi2
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, Volume 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
Benoît Bonnet 1 ; Jean-Paul Gauthier 1 ; Francesco Rossi 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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     author = {Beno{\^\i}t Bonnet and Jean-Paul Gauthier and Francesco Rossi},
     title = {Generic singularities of the {3D-contact} {sub-Riemannian} conjugate locus},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {520--527},
     publisher = {Elsevier},
     volume = {357},
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     year = {2019},
     doi = {10.1016/j.crma.2019.05.008},
     language = {en},
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Benoît Bonnet; Jean-Paul Gauthier; Francesco Rossi. Generic singularities of the 3D-contact sub-Riemannian conjugate locus. Comptes Rendus. Mathématique, Volume 357 (2019) no. 6, pp. 520-527. doi : 10.1016/j.crma.2019.05.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.05.008/

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

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

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

[4] A. Agrachev; G. Charlot; J.-P. Gauthier; V. Zakalyukin 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] A. Agrachev; D. Barilari; U. Boscain A Comprehensive Introduction to Sub-Riemannian Geometry, Cambridge Studies in Advanced Mathematics, 2019

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

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

[8] L. Sacchelli 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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