NASU Institute of Mathematics

Notable research results

The perturbation theory of toroidal invariant manifolds of dynamical systems was developed here by academician M. M. Bogolyubov, Yu. O. Mitropolsky, academician of the NAS of Ukraine and the Russian Academy of Sciences, and A. M. Samoilenko, academician of the NAS of Ukraine. The theory's methods are used to investigate oscillation processes in broad classes of applied problems, in particular, the phenomena of passing through resonance and various bifurcations and synchronizations.

Sharkovsky's order theorem was devised by its author while he worked for the institute. It became the basis for the theory of one-dimensional dynamical systems that enabled the study of chaotic evolutions in deterministic systems, and, in particular, of ‘ideal turbulence’.

The school of the NAS academician Yu. M. Berezansky constructed the theory of generalized functions of infinitely many variables on the basis of spectral approach and operators of generalized translation.

The school of the NAS academician A. V. Skorokhod investigated a broad range of problems related to random processes and stochastic differential equations.

Heuristic methods of phase lumping of complex systems were validated, important results in queuing theory and reliability theory were obtained, and a series of limit theorems for semi-Markov processes were proved by V. S. Korolyuk, academician of the NAS of Ukraine. He has also constructed the Poisson approximation for stochastic homogeneous additive functional with semi-Markov switching.

Directors

• 1934 — 1939 Dmitry Grave
• 1939 — 1941 Mikhail Lavrentyev
• 1941 — 1944 Yurii Pfeiffer, united institute of mathematics and physics
• 1944 — 1948 Mikhail Lavrentyev
• 1948 — 1955 Aleksandr Ishlinskiy
• 1955 — 1958 Boris Gnedenko
• 1958 — 1988 Yurii Mitropolskiy
• 1988 — 2020 Anatoly Samoilenko
• 2021 — Alexander Timokha

Scientific departments

• Algebra
• Analytical mechanics
• Applied researches
• Approximation theory
• Complex analysis and potential theory
• Differential equations and oscillation theory
• Dynamics and stability of multi-dimensional systems
• Fractal Analysis
• Functional Analysis
• Mathematical physics
• Nonlinear analysis
• Numerical mathematics
• Partial differential equations
• Theory of dynamical systems
• Theory of functions
• Theory of random processes
• Topology

Publications

The Institute publishes several scientific journals:

• Methods of Functional Analysis and Topology
• Nonlinear Oscillations
• Symmetry, integrability and Geometry: Methods and Applications (SIGMA)
• Ukrainian Mathematical Journal

References

References

1. "History of the Institute". Institute of Mathematics.