About the Paper by A.I. Lurie on Synchronization Theory

This presentation is devoted to the history of the creation and the contents of not very well-known paper by A.I. Lurie "Certain Problems of Self-synchronization" published in 1970. By this time, some investigations of self-synchronization of unbalanced rotors and pendulum clocks had been carried out mainly by Lurie's pupils. They used the techniques by Poincare, Lyapunov, and asymptotic methods in their investigations. To study this problem A.I. Lurie applied the Hamilton variation principle in conjunction with the method of small parameter and Galerkin's method. Main results were obtained by Lurie in very laconic and elegant form very characteristic for him. This presentation emphasizes the role of Lurie's paper to understand the regularities of frequency self-synchronization and for further development of its theory.