History of Nonlinear Dynamics. Personalia

Aim. The aim of the paper is investigation of the development of the fixed-point method and mapping degree theory associated with the names of P. Bohl, L. Brouwer, K. Borsuk, S. Ulam and others and its application to study of the trajectories of dynamical systems behavior and stable states of ordered media.

Topic.The article reflects important milestones in the history of the physics and mathematics faculty of Saratov University (1917–1945), which played the role of the most important educational and scientific center of the Volga region and the East of Russia. The faculty was established by the Decree of the Provisional Government on July 1 (14), 2017, and began its work from September of the same year.

Aim. The aim of the work is to study the scientific heritage of A.M. Lyapunov from the standpoint of nonlinear physics. Fundamental importance Lyapunov’s contribution is determined not only by the methods he created, which became the basis of the mathematical apparatus in the study of nonlinear phenomena, but his ideas and concepts introduced by him contributed to the formation of concepts and principles of nonlinear dynamics. Method.

The main moments of the historical development of one of the basic methods of nonlinear systems investigating (the averaging method) are traced. This method is understood as a transition from the so-called exact equation: