It determines the property of quasiperiodic auto-oscillation of this system.
The quasiperiodic trajectory 5 of system 2 is said to form an everywhere dense winding of this manifold. The first problem could be solved using perturbation methods Krylov and Bogolyubov , Bogolyubov and Mitropolski , Samoilenko Among perturbation methods used in the theory of quasiperiodic oscillations the most notable is the method of Krylov and Bogolyubov ; see also Bogolyubov and Mitropolski and Bogolyubov et al.
It should be noted that quasiperiodic oscillations are studied not only in models described by ordinary differential equations. Many researchers study such oscillations as solutions of systems of evolution equations with deviating argument, partial differential equations , and equations in infinite-dimensional spaces.
Translated from the Russian original by A. The scientific interests of Samoilenko cover a broad range of important problems in the qualitative theory of differential equations , nonlinear mechanics, and the theory of nonlinear oscillations. His deep results in the theory of multifrequency oscillations, perturbation theory of toroidal manifolds, asymptotic methods of nonlinear mechanics, theory of impulsive systems, theory of differential equations with delay , and theory of boundary-value problems were highly appreciated in Ukraine and abroad.
Academician Samoilenko is the founder of a scientific school in the theory of multifrequency oscillations and theory of impulsive systems recognized by the international mathematical community. His successful many-year guidance of the Institute of Mathematics of the Ukrainian National Academy of Sciences furthers the rapid development of mathematics in the Ukraine and the continuation of the best traditions of the world-known Bogolyubov — Krylov — Mitropolskiy Kyiv scientific school.
Samoilenko gives much attention to training scientists of the highest qualification. For many years, he had given lectures at the Shevchenko Kyiv National University and the " Kyiv Polytechnic Institute " National Technical University and guided the scientific work of postgraduate and doctoral students. Despite the extremely busy schedule of his work as the Director of the Institute of Mathematics of the Ukrainian National Academy of Sciences for about 20 last years since , he has also been the Academician-Secretary of the Department of Mathematics at the National Academy of Sciences of Ukraine , Samoilenko finds time for organizational and public activities.
Many young talents from the "small homeland" of Samoilenko Malynshchyna are grateful to him for founding and heading the charity foundation for support of the development of gifted children and youth. Samoilenko found and taught many nonordinary scientists. He created an international scientific school in differential equations. Among his disciples, there are 33 doctors and 82 candidates of physical and mathematical sciences, who are now researchers of prestigious scientific institutions, professors, heads of chairs, deans, and rectors scientific researchers, pedagogs, and administrators of various levels.
Ilolov , the President of the Tajik Academy of Sciences. Samoilenko is a full member of the National Academy of Sciences of Ukraine  since and the European Academy of Sciences  since From Wikipedia, the free encyclopedia. Bessmertnyi, "Scientists do not need freedom" [in Russian], Newspaper "", No. Invariant Tori [in Russian], Moscow, Nauka Retrieved from " https: Ukrainian scientists Ukrainian mathematicians births Living people. Views Read Edit View history. This page was last edited on 28 August , at Development methods for investigating stability, the study of periodic and almost periodic solutions for such systems A.
Lectures on the theory of oscillations of systems with delay. Institute of Mathematics, Lectures on the analytic theory of differential equations and their applications.
Asymptotic properties of solutions of nonautonomous systems of differential equations of second order. Lectures on the qualitative theory of difference equations.
Differential equations with impulse action. Asymptotic solutions of partial differential equations. Petryshyn cover a broad class of qualitative problems in the theory of nonlinear dynamical systems on a torus. This truth significantly complicates the research of nonlinear oscillations. Main research interests Theory of integral and invariant sets of nonlinear dynamic systems.
Asymptotic solutions of partial differential equations. Periodic and quasi-periodic oscillations of systems with delay. System of evolution equations with periodic and conditionally periodic coefficients.
Elements of the mathematical theory of multi-frequency oscillations: Differential equations with impulse action. Mathematical problems of nonlinear mechanics.
Mathematics and its Applications, V. Kluwer Academic Publishers Group, Systems of evolution equations with periodic and quasiperiodic coefficients.