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Lie group geometry. Invariant metrics and dynamical systems, dual algebra, and their applications in the group analysis of a one-dimensional kinetic equationстатья
Информация о цитировании статьи получена из
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 15 февраля 2024 г.
- Автор: Borovskikh A.V.
- Журнал: Theoretical and Mathematical Physics
- Том: 217
- Год издания: 2023
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 1528
- Последняя страница: 1540
- DOI: 10.1134/S0040577923100082
- Аннотация: On a Lie group, we introduce a family of group-invariant metrics and show that the curves invariant under this group are spirals in all the introduced metrics (i.e., they have constant curvatures). An important role is played by an algebra, which we call dual, defined on the same group. The main relation between these algebras is that the trajectories of the one-parameter groups generated by one algebra are invariant curves in the metric that is invariant under the other algebra. The fact that these curves are spirals distinguishes our approach from that of Cartan, who considered the trajectories of one-parameter groups as geodesics in some metric. The presented results are related to the analysis of the geometric meaning of the previously obtained classification of one-dimensional kinetic equations, where invariant curves are the trajectories of particles.
- Добавил в систему: Боровских Алексей Владиславович