27 апреля 2023 г.

Geometric theory of optimal control


четверг, 16:45


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Samuël Borza


Local non-injectivity of the exponential map at critical points in sub-Riemannian geometry

Аннотация доклада: 

In Riemannian geometry, a theorem originally due to Morse and Littauer states that the exponential map fails to be injective in any neighbourhood of a conjugate vector. Warner also provided an alternative proof of this result by studying some regularity properties and the normal forms of the exponential map. We will discuss a generalisation of these approaches to the sub-Riemannian exponential map and their consequences on the regularity of the sub-Riemannian conjugate locus, as well as on the nature of conjugate points in metric geometry.