ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

# Нелинейная динамика в лицах. История

## Fractal geometry

The article deals with the bases of fractal geometry and fates of its creators. The biographies and the discoveries of Felix Hausdorff and Abram Besicovitch – the main characters of the great play called fractal geometry – are presented with the possible degree of detail. There is no doubt that the author and director of this play was Benoit Mandelbrot. The article presents his biography and brief descriptions of the lives of his predecessors: Henri Poincare, Maurice Gaston Julia and Pierre Gaston Jose Fatou.

## Legacy of Alexander Mikhailovich Lyapunov and nonlinear dynamics

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 study is based on an analysis of Lyapunov’s original works with the involvement of existing literature on his scientific heritage.

## The averaging method, a pendulum with a vibrating suspension: N.N. Bogolyubov, A. Stephenson, P.L. Kapitza and others

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: dx/dt = ?X(t, x),     ? ? is small parameter, to the averaging equation d?/dt= ?X0(?) + ?2P2(?) + ...?mPm(?) by corresponding variable substitution. Bogolyubov–Krylov’s approach to the problem of justifying the averaging method, based on the invariant measure theorem, is analyzed.

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## «Bifurcation chronicle» of saratov university department of physics and mathematics. 1917–1945

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. In the pre-war years, the biological, chemical, geographic and geological departments were separated from the faculty.

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Умер Дмитрий Иванович Трубецков. Прощание состоится 14 августа в 11.30 в Актовом зале 10 корпуса СГУ.