Liouville nonintegrability of sub-Riemannian problems on free Carnot groups of step 4
- Autores: Lokutsievskii L.V.1,2, Sachkov Y.L.3,4
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Afiliações:
- Steklov Mathematical Institute
- Mechanics and Mathematics Faculty
- Ailamazyan Program Systems Institute
- RUDN University
- Edição: Volume 95, Nº 3 (2017)
- Páginas: 211-213
- Seção: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225022
- DOI: https://doi.org/10.1134/S1064562417030048
- ID: 225022
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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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