Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
2.01.1938
Website: https://www.imath.kiev.ua/~sam Keywords: theory of perturbations of invariant manifolds; multifrequency oscillations; Green function for the problem of invariant torus; linear extensions of dynamical systems on a torus; asymptotic methods of nonlinear mechanics; averaging methods; methods of accelerated convergence; impulsive systems; boundary-value problems.
Subject:
The scientific interests cover problems related to the investigation of the behavior of integral curves on invariant toroidal and compact manifolds and in their neighborhoods, the development of the theory of perturbations of toroidal manifolds, the development of asymptotic methods and creation of new methods for investigations in nonlinear mechanics. The notion of the Green function of the problem on the invariant torus of a linear extension of a dynamical system on a torus was introduced. Fundamental results were obtained in the theory of impulsive differential systems. For the investigation of periodic problems for systems of ordinary differential equations, the "numerical-analytic method" was proposed, which was further generalized to a broad class of boundary-value problems.
Main publications:
Ronto M., Samoilenko A. M. Numerical-Analytic Methods in the Theory of Boundary-Value Problems. Singapore: World Scientific Publishing Co., 2000. x+455 pp.
