Founded on February 13, 1934.
Primary research areas of the Institute are:
- theory of nonlinear oscillations;
- mathematical physics;
- theory of ordinary differential equations and partial differential equations;
- theory of nonlinear equations;
- theory of dynamic systems;
- probability theory, mathematical statistics;
- theory of functions;
- complex analysis; development of methods of functional and nonlinear analysis;
- investigation of algebraic and topological structures,
- analytical mechanics, dynamics of special mechanical systems;
- development of numerical methods to investigate mechanical and physical problems.
Main achievements and research results:
The perturbation theory of toroidal invariant manifolds of dynamical systems was constructed; its methods enable one to investigate oscillation processes in broad classes of applied problems, in particular, the phenomena of passing through resonance and various bifurcations and synchronizations (academician M. M. Bogolyubov, Yu. O. Mitropolsky, academician of NAS and the Russian Academy of Sciences, and A. M. Samoilenko, NAS academician). Sharkovsky’s order theorem became the basis for today’s theory of one-dimensional dynamical systems, which permitted studying chaotic evolutions in deterministic systems, and, in particular, the ‘ideal turbulence’. The school of 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 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, a series of limit theorems for semi-Markov processes were proved, and the Poisson approximation for stochastic homogeneous additive functionals with semi-Markov switchings was constructed (V. S. Korolyuk, NAS academician).
