Аннотация:The article presents the biography of Alexander A. Shestakov — ScD in Physics and Mathematics, Professor, a major scientist who had a wide range of scientific interests. His researches are devoted to the key problems of quality theory of differential equations, stability theory of dynamic systems, and also various applied aspects of these theories to problems of dynamics of transport systems. Professor Shestakov and his students and followers have obtained significant results in various fields of fundamental and applied mathematics, as well as mechanics. The article provides a brief overview of the scientific and pedagogical heritage of the scientist who is an organizer and founder of the famous scientific school on quality theory of dynamic processes and stability theory of differential equation solutions. He and his numerous students obtained fundamental results related to the development of the theory of stability in the sense of A.M. Lyapunov and the theory of stability in the sense of N.E. Zhukovsky, with the development of methods for the analysis of orbital stability, limitation and convergence of solutions of differential equations, with the development of limit equations and method of localization of limit sets, with theoretical and applied problems of stability of mathematical models of dynamics of railway transport. Its manuals, textbooks and monographs are the standard of fundamentality of the issues presented in them and have not lost their relevance to our days.
