5 papers
Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups with three-dimensional generating distributions
Valera Berestovskii, Irina Zubareva
We find three-dimensional subspaces of four-dimensional connected Lie algebras, generating these algebras, and abnormal extremals on connected Lie groups with these Lie algebras an…
Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups
Valera Berestovskii, Irina Zubareva
Abnormal extremals on four-dimensional connected Lie groups with left-invariant sub-Finsler quasimetric, defined by a seminorm on a two-dimensional subspace of the Lie algebra gene…
Extremals of a left-invariant sub-Finsler quasimetric on the Cartan group
Valera Berestovskii, Irina Zubareva
Using the Pontryagin Maximum Principle for the time-optimal problem in coordinates of the first kind, we find extremals of abitrary left-invariant sub-Finsler quasimetric on the Ca…
Extremals of a left-invariant sub-Finsler metric on the Engel group
Valera Berestovskii, Irina Zubareva
The authors found extremals of arbitrary left-invariant sub-Finsler metric on the Engel group defined by a distribution of rank two. They use for this the Pontryagin Maximum Princi…
Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups
Valera Berestovskii, Irina Zubareva
On the ground of origins of the theory of Lie groups and Lie algebras, their (co)adjoint representations, and the Pontryagin maximum principle for the time-optimal problem are give…