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A dynamical approach to the Sard problem in Carnot groups. (English) Zbl 1440.53035

Summary: We introduce a dynamical-systems approach for the study of the Sard problem in sub-Riemannian Carnot groups. We show that singular curves can be obtained by concatenating trajectories of suitable dynamical systems. As an application, we positively answer the Sard problem in some classes of Carnot groups.

MSC:

53C17 Sub-Riemannian geometry
37N35 Dynamical systems in control
58K05 Critical points of functions and mappings on manifolds
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