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On stability of generic subriemannian caustic in the three-space. (English. Abridged French version) Zbl 0992.53023

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.

MSC:

53C17 Sub-Riemannian geometry
58K25 Stability theory for manifolds
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