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pro vyhledávání: '"Sachkov, Yu. L."'
Autor:
Galyaev, I. A., Sachkov, Yu. L.
Two left-invariant Lorentzian problems on the Heisenberg group are considered. The Pontryagin maximum principle was applied to both problems and a parameterization of abnormal and normal extremal trajectories was obtained. Reachability sets and the e
Externí odkaz:
http://arxiv.org/abs/2407.07379
Autor:
Ali, A. Z., Sachkov, Yu. L.
In this paper, we study a two-dimensional Lorentzian problem on the anti-de Sitter plane. Using methods of geometric control theory and differential geometry, it was possible to construct an orthonormal frame, calculate extremal trajectories, describ
Externí odkaz:
http://arxiv.org/abs/2407.07172
Autor:
Sachkov, Yu. L.
Two flat sub-Lorentzian problems on the Martinet distribution are studied. For the first one, the attainable set has a nontrivial intersection with the Martinet plane, but for the second one it does not. Attainable sets, optimal trajectories, sub-Lor
Externí odkaz:
http://arxiv.org/abs/2407.04341
Autor:
Sachkov, Yu. L.
Left-invariant Lorentzian structures on the 2D solvable non-Abelian Lie group are studied. Sectional curvature, attainable sets, Lorentzian length maximizers, distance, spheres, and infinitesimal isometries are described.
Externí odkaz:
http://arxiv.org/abs/2307.07706
Autor:
Sachkov, Yu. L., Sachkova, E. F.
The left-invariant sub-Lorentzian problem on the Heisenberg group is considered. An optimal synthesis is constructed, the sub-Lorentzian distance and spheres are described.
Comment: 28 pages, 22 figures
Comment: 28 pages, 22 figures
Externí odkaz:
http://arxiv.org/abs/2208.04073
We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for arbitrary $\Omeg
Externí odkaz:
http://arxiv.org/abs/2004.10194
Akademický článek
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Autor:
Sachkov, Yu. L.1 (AUTHOR) yusachkov@gmail.com
Publikováno v:
Differential Equations. Dec2023, Vol. 59 Issue 12, p1769-1777. 9p.
Autor:
Ardentov, A. A., Sachkov, Yu. L.
We consider the nilpotent left-invariant sub-Riemannian structure on the Engel group. This structure gives a fundamental local approximation of a generic rank 2 sub-Riemannian structure on a 4-manifold near a generic point (in particular, of the kine
Externí odkaz:
http://arxiv.org/abs/1710.00216
Autor:
Podobryaev, A. V., Sachkov, Yu. L.
Publikováno v:
Journal of Dynamical and Control Systems, 24:3 (2018), 391-423
We consider the Lie group PSL(2) (the group of orientation preserving isometries of the hyperbolic plane) and a left-invariant Riemannian metric on this group with two equal eigenvalues that correspond to space-like eigenvectors (with respect to the
Externí odkaz:
http://arxiv.org/abs/1701.00825