Liouville nonintegrability of sub-Riemannian problems on free Carnot groups of step 4


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Resumo

One of the main approaches to the study of the Carnot–Carathéodory metrics is the Mitchell–Gromov nilpotent approximation theorem, which reduces the consideration of a neighborhood of a regular point to the study of the left-invariant sub-Riemannian problem on the corresponding Carnot group. A detailed analysis of sub-Riemannian extremals is usually based on the explicit integration of the Hamiltonian system of Pontryagin’s maximum principle. In this paper, the Liouville nonintegrability of this system for left-invariant sub-Riemannian problems on free Carnot groups of step 4 and higher is proved.

Sobre autores

L. Lokutsievskii

Steklov Mathematical Institute; Mechanics and Mathematics Faculty

Autor responsável pela correspondência
Email: lion.lokut@gmail.com
Rússia, Moscow, 119991; Moscow, 119991

Yu. Sachkov

Ailamazyan Program Systems Institute; RUDN University

Email: lion.lokut@gmail.com
Rússia, Yaroslavskaya obl., Pereslavskii raion, s. Ves’kovo, 152021; Moscow, 117198

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