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8 Gubkina St. Moscow,
119991, Russia
Tel.: +7(495) 984 81 41
Fax: +7(495) 984 81 39
Web site: www.mi-ras.ru
E-mail: steklov@mi-ras.ru

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Department of Differential Equations

| Seminars | History of the Department | Research Directions | Awards and Prizes Received by Members of the Department | Publications |
Staff
Aseev Sergei Mironovich

Doctor Phys.-Math. Sci., Corresponding Member of RAS, Head of Department, Chief Scientific Researcher
office: 423; tel.: +7 (495) 984 81 41 * 37 75; e-mail: aseev@mi-ras.ru
Principal fields of research: Optimal control. Dynamic systems. Differential inclusions. Multivalued mappings. Nonsmooth analysis. Mathematical economics.
Aseev Sergei Mironovich
Besov Konstantin Olegovich

Candidate Phys.-Math. Sci., Senior Scientific Researcher
office: 522; tel.: +7 (499) 941 01 93, +7 (495) 984 81 41 * 36 92; e-mail: kbesov@mi-ras.ru
Principal fields of research: Nonlinear partial differential equations, optimal control, optimal economic growth problems.
Besov Konstantin Olegovich
Bufetov Aleksandr Igorevich

Doctor Phys.-Math. Sci., Leading Scientific Researcher
office: 438; tel.: +7 (495) 984 81 41 * 39 92; e-mail: bufetov@mi-ras.ru
Principal fields of research: Ergodic theory.
Bufetov Aleksandr Igorevich
Gamkrelidze Revaz Valerianovich

Doctor Phys.-Math. Sci., Professor, Academician of RAS, Chief Scientific Researcher
office: 420; tel.: +7 (495) 984 81 41 * 39 35; e-mail: gam@mi-ras.ru
Principal fields of research: Variation calculus. Theory of optimal control. Differential-geometrical methods in the theory of extreme problems. Chronological calculus. Differential games.
Gamkrelidze Revaz Valerianovich
Klimenko Alexey Vladimirovich

Candidate Phys.-Math. Sci., Scientific Researcher
office: 424; tel.: +7 (495) 984 81 41 * 37 75; e-mail: klimenko@mi-ras.ru
Principal fields of research: Ergodic theorems for group actions, Markov partitions.
Klimenko Alexey Vladimirovich
Lokutsievskiy Lev Vyacheslavovich

Doctor Phys.-Math. Sci., Leading Scientific Researcher
office: 420; tel.: +7 (495) 984 81 41 * 39 35; e-mail: lion@mi-ras.ru
Principal fields of research: Nonequilibrium statistical mechanics. Dynamical systems theory.
Lokutsievskiy Lev Vyacheslavovich
Nikolskii Mikhail Sergeevich

Doctor Phys.-Math. Sci., Professor, Leading Scientific Researcher
office: 439; tel.: +7 (499) 941 01 80, +7 (495) 984 81 41 * 36 77; e-mail: mni@mi-ras.ru
Principal fields of research: Qualitative problems of the theory of optimal control. The theory of differential games.
Nikolskii Mikhail Sergeevich
Osipov Yurii Sergeevich

Doctor Phys.-Math. Sci., Professor, Academician of RAS, Chief Scientific Researcher
tel.: +7 (495) 954 35 06;
Principal fields of research: Optimal control for systems with distributed parameters. Inverse problems of dynamics. Differential games.
Osipov Yurii Sergeevich

Agrachev Andrei Aleksandrovich

Doctor Phys.-Math. Sci., Out-Of-Staff Member
office: 420; tel.: +7 (495) 984 81 41 * 39 35; e-mail: agrachev@mi-ras.ru
Principal fields of research: Variational calculus. Optimal control theory. Differential and geometric methods in theory of extremal problems. Chronological calculus.
Agrachev Andrei Aleksandrovich
Grigorchuk Rostislav Ivanovich

Doctor Phys.-Math. Sci., Professor, Out-Of-Staff Member
e-mail: grigorch@math.tamu.edu
Personal page: http://www.math.tamu.edu/~grigorch/
Principal fields of research: Ergodic theory of noncommutative groups of transformations.
Grigorchuk Rostislav Ivanovich
Il'yashenko Yulii Sergeevich

Doctor Phys.-Math. Sci., Professor, Out-Of-Staff Member
e-mail: yulijs@mccme.ru
Principal fields of research: Dynamical systems. Attractors. Bifurcation theory. Relaxation oscilations. Limit cycles. Abelian integrals.
Il'yashenko Yulii Sergeevich
Kuksin Sergei Borisovich

Doctor Phys.-Math. Sci., Leading Scientific Researcher
e-mail: S.B.Kuksin@ma.hw.ac.uk
Ledyaev Yurii Semenovich

Doctor Phys.-Math. Sci., Professor, Out-Of-Staff Member
e-mail: ledyaev@mi-ras.ru
Principal fields of research: Optimal control and differential games. Nnonsmooth and nonlinear analysis. Differential inclusions and inequalities. Robust discontinuous feedback in stabilization of control systems. Optimal control and differential games.
Ledyaev Yurii Semenovich
Mishchenko Aleksandr Sergeevich

Doctor Phys.-Math. Sci., Professor, Out-Of-Staff Member
e-mail: asmisch@mi-ras.ru
Principal fields of research: Algebraic and differential topology. Operator and C*-algebras. Index theory, K-theory. Dynamic systems. Mathematical modelling in ecology. Bioinformatics. Mathematical education.
Mishchenko Aleksandr Sergeevich

Anosov Dmitrii Viktorovich (30.11.1936 – 05.08.2014)

Doctor Phys.-Math. Sci., Professor, Academician of RAS

Principal fields of research: Dynamical systems. Ergodicity. Structural stability. Asymptotics. Coverings. Monodromy.
Anosov Dmitrii Viktorovich (30.11.1936 – 05.08.2014)
Bolibrukh Andrey Andreevich (30.01.1950 – 11.11.2003)

Doctor Phys.-Math. Sci., Professor, Academician of RAS

Principal fields of research: Fuchsian equations; monodromy; singular points; the Riemann–Hilbert problem; the Birkhoff standard form; isomonodromic deformations; the Painleve equations; vector bundles; logarithmic connections.
Bolibrukh Andrey Andreevich (30.01.1950 – 11.11.2003)
Kryazhimskii Arkadii Viktorovich (02.01.1949 – 03.11.2014)

Doctor Phys.-Math. Sci., Professor, Academician of RAS

Principal fields of research: Global optimization methods. Optimal control. Dynamical games. Inverse problems of dynamics of control systems and their applications to economic problems and environment.
Kryazhimskii Arkadii Viktorovich (02.01.1949 – 03.11.2014)
Mishchenko Evgenii Frolovich (09.03.1922 – 20.07.2010)

Doctor Phys.-Math. Sci., Academician of RAS

Principal fields of research: Singular perturbations. Control problems. Differential games. Duality. Topology.
Mishchenko Evgenii Frolovich (09.03.1922 – 20.07.2010)
Pontryagin Lev Semenovich

Doctor Phys.-Math. Sci., Professor, Academician of RAS

Principal fields of research: Topology, Differential equations, Optimal control, Differential games.
Pontryagin Lev Semenovich
Top
Seminars
Seminar "Optimal Control and Dynamical Systems"
Steklov Mathematical Institute of RAS, Room 430 (8 Gubkina)
Geometric Theory of Optimal Control
Lomonosov Moscow State Univ, Main Building, Faculty of Mechanics and Mathematics, auditorium 14-05
Globus Seminar
IUM (Bolshoi Vlas'evskii per., 11)
Problems of Mathematical Control Theory
Seminar organizers: S. M. Aseev; M. S. Nikol'skii
Steklov Mathematical Institute, Room 430 (8 Gubkina)
Seminar on analytic theory of differential equations
Steklov Mathematical Institute, Room 440 (8 Gubkina)
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History of the Department

Department of Differential Equations (Department of Ordinary Differential Equations before 2002) was created in1959 by L.S.Pontryagin, who headed the department until his death in1988.

Up to the early 1950s, L.S.Pontryagin was mainly focused on topology. However, later he decided to change his field of research and turned to ordinary differential equations and related problems (including those connected with control theory, which was calledand representedautomatic control theory at that time). To discuss these problems, in fall1952, Pontryagin organized a seminar at the Steklov Institute (Pontryagin led this seminar together with his younger colleagues V.G.Boltyanskii, R.V.Gamkrelidze, and E.F.Mishchenko). Later, the seminar gave rise to several other seminars while continuing as the main seminar of the department.

In the new area, L.S.Pontryagin had four fields of interest at different times:

  • singular perturbation theory,
  • stability of equilibrium states of relay systems,
  • mathematical theory of optimal processes,
  • differential games.

Of these investigations, the most renowned and recognized are Pontryagin's studies on optimal modes in control processes. Everything started with several mathematical models of specific problems that were presented by engineers at Pontryagin's seminar. Up to1955, Pontryagin found a necessary optimality condition, now known as the Pontryagin maximum principle. For a wide class of linear systems, the maximum principle was proved by R.V.Gamkrelidze in1957. In1958, V.G.Boltyanskii proved it in the general case. And already in1961, Pontryagin, Boltyanskii, Gamkrelidze, and Mishchenko wrote the monograph Mathematical Theory of Optimal Processes, for which the entire group received the country's highest scientific award, the Lenin Prize. Since then optimal control theory has grown into a separate field of research in theoretical and applied mathematics.

Among outstanding results obtained in the department, one should point out the following:

  • L.S.Pontryagin and E.F.Mishchenko's studies on the theory of relaxation oscillations and differential games;
  • Yu.S.Osipov and A.V.Kryazhimskiy's studies on differential games, inverse problems in dynamics, and optimization theory;
  • D.V.Anosov's studies on the properties of geodesic flows on closed Riemann surfaces of negative curvature, on averaging in systems of differential equation with rapidly oscillating solutions, and on the behavior at infinity of the lifts (to the universal covering surfaces) of trajectories of flows on closed surfaces;
  • Negative solution of the RiemannHilbert problem (of Hilbert's 21st problem for linear Fuchsian systems), which was obtained by A.A.Bolibruch in1989, as well as Bolibruch's studies on isomonodromic deformations of Fuchsian systems;
  • A.A.Agrachev and R.V.Gamkrelidze's studies on geometric theory of optimal control and related problems of differential geometry, calculus of variations, and Hamiltonian dynamics;
  • S.M.Aseev's results on regularization of nonsmooth dynamic optimization problems, multivalued analysis, and mathematical theory of optimal economic growth problems.

In 19881997 the department was headed by R.V.Gamkrelidze, and in 19972014, by D.V.Anosov.

Since February 2014, the department is headed by S. M. Asseev.

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Research Directions

At present the department is developing the following fields of research:

  • dynamical systems, ergodicity, structural stability, asymptotics (D. V. Anosov, A. I. Bufetov, A. V. Klimenko);
  • Differential and geometric methods in the theory of extremal problems (A. A. Agrachev, R. V.  Gamkrelidze);
  • optimal economic growth problems (S. M. Aseev, K. O. Besov, A. V. Kryazhimskiy, M. S. Nikol'skii);
  • optimal control, differential games, inverse problems of the dynamics of control systems (A. V. Kryazhimskiy, Yu. S. Osipov, M. S. Nikol'skii).

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Awards and Prizes Received by Members of the Department

In 1962, the group headed by L.S.Pontryagin and consisting of V.G.Boltyanskii, R.V.Gamkrelidze, and E.F.Mishchenko was awarded the Lenin Prize for the "Cycle of studies on ordinary differential equations and their applications to optimal control theory and oscillation theory in 19561961".

D. V. Anosov:
Moscow Mathematical Society award 1965,
USSR State Prize 1976,
Humboldt Foundation Research Award 1999,
A. M. Lyapunov Prize of the Russian Academy of Sciences 2001
Yu. S. Osipov:
Lenin Prize 1976,
State Prize of the Russian Federation 1993,
L. Euler Gold Medal 1997,
The Order For Merit to the Fatherland 1999
A. A. Bolibruch:
A. M. Lyapunov Prize of the Russian Academy of Sciences 1995,
State Prize of the Russian Federation 2001
R. I. Grigorchuk:
Moscow Mathematical Society award 1980
A. S. Mishchenko:
State Prize of the Russian Federation 1996 (jointly with A.T.Fomenko),
Lomonosov Prize 2001
K. O. Besov:
MAIK "Nauka/Interperiodika" Prize for the cycle of papers on the blow-up of solutions to quasilinear parabolic systems 2005

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