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Makarov Evgenii Konstantinovich

Statistics Math-Net.Ru
Total publications: 35
Scientific articles: 34

Number of views:
This page:717
Abstract pages:1885
Full texts:676
References:156
Professor
Doctor of physico-mathematical sciences (2001)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 06.08.1963
E-mail:
Keywords: linear systems of ordinary differential equations; Lyapunov characteristic exponents; total differential equations; control problems for Lyapunov exponents; vector optimization.

Subject:

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.

Biography

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.

   
Main publications:
  • Makarov E. K., Rachkovski N. N. Efficient sets of convex compacta are arcwise connected // J. Optimiz. Theory and Appl., 2001, 110(1), 159–172.

http://www.mathnet.ru/eng/person17583
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/231860

Publications in Math-Net.Ru
1. On upward mobility of the highest exponent of a linear differential system under perturbations of the coefficients from the simplest classes with degeneracies
E. K. Makarov, I. V. Marchenko
Tr. Inst. Mat., 25:2 (2017),  50–59
2. On the definition of uniform complete controllability
E. K. Makarov, S. N. Popova
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:3 (2017),  326–343
3. On stationary solutions for Lindblad-type equations
S. Ya. Kilin, E. K. Makarov
Tr. Inst. Mat., 22:2 (2014),  53–62
4. Axiomatic representation for smallness classes of coefficient perturbations to linear differential systems
E. K. Makarov
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 1,  46–57
5. Asymptotics of the solution of the main problem of the integral fire theory
A. K. Demenchuk, E. K. Makarov
Differ. Uravn., 46:1 (2010),  23–28
6. Forced oscillations of relativistic oscillator with periodic external exitation
E. K. Makarov, A. A. Afanas'ev, A. N. Rubinov
Tr. Inst. Mat., 17:1 (2009),  103–109
7. A solution for the problem on oscillations of quasi-relativistic oscillator with periodic external exitation
E. K. Makarov, A. A. Afanas'ev, A. N. Rubinov
Tr. Inst. Mat., 16:2 (2008),  76–84
8. On radial solutions of completely integrable total differential equations
E. K. Makarov
Differ. Uravn., 42:10 (2006),  1318–1323
9. On the critical parameter value for the higher sigma-exponent of linear differential systems
E. K. Makarov
Differ. Uravn., 42:6 (2006),  844–846
10. On the properties of bogdanov perturbations of linear differential systems
E. K. Makarov
Differ. Uravn., 42:2 (2006),  275–277
11. Problems of control over Lyapunov invariants
V. A. Zaitsev, E. K. Makarov, S. N. Popova, E. L. Tonkov
Izv. IMI UdGU, 2006, no. 3(37),  43–48
12. On an Algorithm for Constructing an Attainable Upper Boundary for the Higher Exponent of Perturbed Systems
E. K. Makarov, I. V. Marchenko
Differ. Uravn., 41:12 (2005),  1621–1634
13. On an Upper Bound for the Higher Exponent of a Linear Differential System with Integrable Perturbations on the Half-Line
E. K. Makarov, I. V. Marchenko, N. V. Semerikova
Differ. Uravn., 41:2 (2005),  215–224
14. The Characteristic Sets of Multidimensional Equations with Respect to a Polyhedral Cone Can Be Nonclosed
E. K. Makarov
Differ. Uravn., 39:4 (2003),  560–562
15. Sufficient Conditions for the Local Proportional Controllability of Lyapunov Exponents of Linear Systems
E. K. Makarov, S. N. Popova
Differ. Uravn., 39:2 (2003),  217–226
16. The Complete Integrability of the Linear Approximation Equations for Completely Integrable Quasilinear Total Differential Equations
E. K. Makarov
Differ. Uravn., 36:12 (2000),  1631–1635
17. On the higher exponent of a linear many-dimensional completely integrable equation
E. K. Makarov
Differ. Uravn., 36:1 (2000),  54–61
18. On the global controllability of a complete set of Lyapunov invariants of two-dimensional linear systems
E. K. Makarov, S. N. Popova
Differ. Uravn., 35:1 (1999),  97–106
19. On the global controllability of central exponents of linear systems.
E. K. Makarov, S. N. Popova
Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 2,  60–67
20. On the existence of weakly normal bases of solutions of linear multidimensional completely integrable equations
E. K. Makarov
Differ. Uravn., 34:12 (1998),  1703–1705
21. On the discreteness of asymptotic invariants of linear differential systems
E. K. Makarov
Differ. Uravn., 34:10 (1998),  1322–1331
22. On boundedness conditions for characteristic sets of solutions of linear multidimensional equations
E. K. Makarov
Differ. Uravn., 33:5 (1997),  653–657
23. Local controllability of characteristic Lyapunov exponents of systems with simple exponents
E. K. Makarov, S. N. Popova
Differ. Uravn., 33:4 (1997),  495–499
24. On weakly regular linear completely solvable multidimensional equations
E. K. Makarov
Differ. Uravn., 33:2 (1997),  221–225
25. On the realization of partial exponents of solutions of linear differential systems on geometric progressions
E. K. Makarov
Differ. Uravn., 32:12 (1996),  1710–1711
26. Malkin estimates for the norm of the Cauchy matrix of a linear differential system
E. K. Makarov
Differ. Uravn., 32:3 (1996),  328–334
27. On the structure of characteristic sets of solutions of linear completely solvable total differential equations
E. K. Makarov
Differ. Uravn., 31:2 (1995),  220–227
28. On the interrelation between characteristic functionals and weak characteristic exponents
E. K. Makarov
Differ. Uravn., 30:3 (1994),  393–399
29. The effect of Lyapunov transforms and different perturbations on the nonregularity sets of linear differential systems
E. K. Makarov
Differ. Uravn., 28:10 (1992),  1708–1715
30. On a criterion for joint behavior of higher sigma exponents of a triangular system and the system of its diagonal approximation
E. K. Makarov
Differ. Uravn., 27:5 (1991),  910–911
31. A remark on sets of nonregularity of almost periodic linear differential systems
E. K. Makarov
Differ. Uravn., 27:3 (1991),  539–541
32. Linear systems with nonregularity sets of full measure
E. K. Makarov
Differ. Uravn., 25:2 (1989),  209–212
33. Sets of irregularity of linear systems with a parameter multiplying the derivative
E. K. Makarov
Differ. Uravn., 24:12 (1988),  2091–2098
34. Lyapunov irregular linear systems with a parameter multiplying the derivative
N. A. Izobov, E. K. Makarov
Differ. Uravn., 24:11 (1988),  1870–1880
35. A case of time-optimality for a linear homogeneous system
E. K. Makarov
Differ. Uravn., 22:2 (1986),  203–208

36. 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
37. 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

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