01.01.02 (Differential equations, dynamical systems, and optimal control)
linear systems of ordinary differential equations; Lyapunov characteristic exponents; total differential equations; control problems for Lyapunov exponents; vector optimization.
Properties of Lyapunov irregularity sets for linear ordinary differential systems with parameter under derivative are investigated. Sufficient conditions for discretizability of asymptotic invariants of linear differential systems are proved. Interrelations between characteristic exponents and characteristic functionals of linear total differential equations are established. By means of these interrelations the structure of characteristic sets of such equations is investigated including sufficient conditions for closedness and boundednes. Sufficient conditions for complete integrability of linear approximation to nonlinear completely integrable total differential equation are proved. These condition holds e.g. for each equation with $C^1$ right part. A number of papers (with S. N. Popova)are dedicated to control problems for Lyapunov exponent and other asymptotic invariants of uniformly completely controllable linear systems. These problems are the generalization of classical pole assignment problem to the settings of non-autonomous system. Sufficient conditions for local and global controllability of the invariants under consideration are obtained. A number of papers (with N. N. Rachkovski) are dedicated to vector optimization theory. Arcwise connectedness of the efficient point set of convex compactum in any Hausdorff topological vector space is proved; exhaustive comparison theorems for various kinds of proper efficiency in normed linear space are obtained; density results for generalized Henig proper efficiency under the weakest suppositions are proved.
Graduated from Faculty of Mathematics and Mechanics of Byelorussian State University (BSU) in 1985 (department of differential equations). Ph.D. thesis was defended in 1989. D.Sci. thesis was defended in 2001. A list of my works contains more than 70 titles.
Makarov E. K., Rachkovski N. N. Efficient sets of convex compacta are arcwise connected // J. Optimiz. Theory and Appl., 2001, 110(1), 159–172.
In memory of Evgenii Leonidovich Tonkov (27.06.1940–28.09.2014) I. V. Gaishun, A. A. Gryzlov, V. Ya. Derr, N. A. Izobov, A. I. Karpov, E. K. Makarov, G. V. Merzlyakova, N. N. Petrov, S. N. Popova, L. I. Rodina, N. Kh. Rozov, I. N. Sergeev, A. A. Tolstonogov, V. N. Ushakov, A. G. Chentsov Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4, 146–154
Nikolai Alekseevich Izobov (A tribute in honor of his 70th birthday) A. V. Arutyunov, Yu. N. Bibikov, F. P. Vasil'ev, I. V. Gaishun, S. V. Emel'yanov, V. A. Il'in, I. T. Kiguradze, S. K. Korovin, L. D. Kudryavtsev, A. B. Kurzhanskii, S. A. Mazanik, E. K. Makarov, A. A. Martynyuk, E. F. Mishchenko, E. I. Moiseev, Yu. S. Osipov, V. A. Pliss, N. Kh. Rozov, V. A. Sadovnichy, A. M. Samoilenko, T. K. Shemjakina Differ. Uravn., 46:1 (2010), 3–8