Brief Survey of Studies Related to the Appearance of the Problem of Chaotic and Stochastic Motions and to Turbulence Theory

Abstract

Until quite recently, all phenomena in the world were separated into deterministic and random. The theory of differential equations, mathematical physics, classical mechanics, and electro-dynamics studied the former; probability theory, the theory of random processes, statistical physics, and quantum mechanics, the latter. This sharp borderline seemed unquestionable, and raised no doubts, though certain discrepancies did arise: The probabilistic nature of classical statistical physics laws was not justified accurately, and was accounted for by the very large number of particles and degrees of freedom.