


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; email: aseev@miras.ru Principal fields of research:
Optimal control. Dynamic systems. Differential inclusions. Multivalued mappings. Nonsmooth analysis. Mathematical economics.


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; email: kbesov@miras.ru Principal fields of research:
Nonlinear partial differential equations, optimal control, optimal economic growth problems.


Bufetov Aleksandr Igorevich Doctor Phys.Math. Sci., Leading Scientific Researcher
office: 438; tel.: +7 (495) 984 81 41 * 39 92; email: bufetov@miras.ru Principal fields of research:
Ergodic theory.


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


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


Kuksin Sergei Borisovich Doctor Phys.Math. Sci., Leading Scientific Researcher
office: 420; tel.: +7 (495) 984 81 41 * 39 35; email: S.B.Kuksin@ma.hw.ac.uk


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


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; email: mni@miras.ru Principal fields of research:
Qualitative problems of the theory of optimal control. The theory of differential games.


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.



Agrachev Andrei Aleksandrovich Doctor Phys.Math. Sci., OutOfStaff Member
office: 440; email: agrachev@miras.ru Principal fields of research:
Variational calculus. Optimal control theory. Differential and geometric methods in theory of extremal problems. Chronological calculus.


Grigorchuk Rostislav Ivanovich Doctor Phys.Math. Sci., Professor, OutOfStaff Member
email: grigorch@math.tamu.edu Personal page: http://www.math.tamu.edu/~grigorch/
Principal fields of research:
Ergodic theory of noncommutative groups of transformations.


Il'yashenko Yulii Sergeevich Doctor Phys.Math. Sci., Professor, OutOfStaff Member
email: yulijs@mccme.ru Principal fields of research:
Dynamical systems. Attractors. Bifurcation theory. Relaxation oscilations. Limit cycles. Abelian integrals.


Ledyaev Yurii Semenovich Doctor Phys.Math. Sci., Professor, OutOfStaff Member
email: ledyaev@miras.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.


Mishchenko Aleksandr Sergeevich Doctor Phys.Math. Sci., Professor, OutOfStaff Member
email: asmisch@miras.ru Principal fields of research:
Algebraic and differential topology. Operator and C*algebras. Index theory, Ktheory. Dynamic systems. Mathematical modelling in ecology. Bioinformatics. Mathematical education.



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.


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.


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.


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.


Pontryagin Lev Semenovich Doctor Phys.Math. Sci., Professor, Academician of RAS
Principal fields of research:
Topology, Differential equations, Optimal control, Differential games.



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Seminars

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History of the Department
Department of Differential Equations (Department of Ordinary Differential
Equations before 2002) was created in 1959 by
L. S. Pontryagin, who headed the department until his death
in 1988.
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 called—and
represented—automatic control theory at that time). To discuss these
problems, in fall 1952, 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 to 1955, 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 in 1957. In 1958,
V. G. Boltyanskii proved it in the general case. And already
in 1961, 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 Riemann–Hilbert problem (of Hilbert's 21st
problem for linear Fuchsian systems), which was obtained by
A. A. Bolibruch in 1989, 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 1988–1997 the department was headed by
R. V. Gamkrelidze, and in 1997–2014, 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 1956–1961".
 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 blowup of solutions to quasilinear parabolic systems — 2005

List of publications

