Fronts of control-affine systems in R^3

Journal of Singularities
volume 21 (2020), 15-29

Received: 30 April 2018. Received in revised form: 17 March 2019.

DOI: 10.5427/jsing.2020.21b

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Abstract:

We consider a control-affine system in three-dimensional space with control parameters belonging to a two-dimensional disk and study its fronts evolving from a point for small times. We prove that generically the Legendrian lifts of such fronts have standard singularities and there are only two principally different typical cases --- hyperbolic and elliptic.

Author(s) information:

Ilya Bogaevsky
Faculty of Mechanics and Mathematics
Lomonosov Moscow State University
Leninskie Gory
Moscow GSP-1, 119991, Russia

Scientific Research Institute for System Analysis of RAS
Moscow, Russia