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

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. © 2017, Pleiades Publishing, Ltd.

Авторы
Lokutsievskii L.V.1, 2 , Sachkov Y.L. 3, 4
Журнал
Номер выпуска
3
Язык
Английский
Страницы
211-213
Статус
Опубликовано
Том
95
Год
2017
Организации
  • 1 Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991, Russian Federation
  • 2 Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russian Federation
  • 3 Ailamazyan Program Systems Institute, Russian Academy of Sciences, Yaroslavskaya obl., Pereslavskii raion, s. Ves’kovo, 152021, Russian Federation
  • 4 RUDN University, Moscow, 117198, Russian Federation
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5538/
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Vosskresensky L.G., Titov A.A., Samavati R., Kobzev M.S., Dorovatovskii P.V., Khrustalev V.N., Hong H.C., Thi T.A.D., Van T.N., Sorokina E.A., Varlamov A.V.
Химия гетероциклических соединений. Латвийский институт органического синтеза Латвийской академии наук / Springer New York Consultants Bureau. Том 53. 2017. С. 575-581