Current Research

Invariant control systems

Equivalence (detached feedback and state space); classification (invariant systems on 3D and 4D Lie groups); controllability; invariant optimal control problems (on low-dimension Lie groups); equivalence of invariant optimal control problems (cost equivalence).

Quadratic Hamilton-Poisson systems

Equivalence (linear and affine); classification (homogeneous and inhomogeneous systems on 3D and 4D Lie-Poisson spaces); Lyapunov stability; explicit integration (by elliptic functions).

Invariant Riemannian and sub-Riemannian geometry

Equivalence (under isometries and isometric group automorphisms); classification (invariant structures on low-dimensional Lie groups); explicit integration of geodesic equations.

Nonholonomic Riemannian geometry

Equivalence (under nonholonomic isometries); classification (invariant structures on low-dimensional Lie groups); curvature of structures (particularly, the Schouten and Wagner curvature tensors).

Geometry of homogeneous spaces

Homogeneous spaces of low dimension; curves and surfaces (method of moving frames); invariant connections.


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Last Modified: Fri, 11 May 2018 16:19:52 SAST