Agrachev, Andrei A.; Charlot, Grégoire; Gauthier, Jean-Paul A.; Zakalyukin, Vladimir M. On stability of generic subriemannian caustic in the three-space. (English. Abridged French version) Zbl 0992.53023 C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 6, 465-470 (2000). By studying the singularities of exponential mappings in sub-Riemannian geometry in the 3-dimensional contact case, the authors show here that the corresponding generic caustics have moduli at the origin. The graph of the multivalued arclength function, reparametrized in a certain way, is a 3-dimensional surface which has the natural structure of a wave front. A stability result for this object (called the big wave front) is obtained. Reviewer: Cornelia-Livia Bejan (Iaşi) MSC: 53C17 Sub-Riemannian geometry 58K25 Stability theory for manifolds Keywords:sub-Riemannian geometry; module for caustics; wave front PDFBibTeX XMLCite \textit{A. A. Agrachev} et al., C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 6, 465--470 (2000; Zbl 0992.53023) Full Text: DOI