Quasi-random dynamical systems

This paper is the author's abstract of his dissertation for the degree Doctor of Physiomathematical Science. The dissertation was defended on March 7, 1969, in the Study of the Soviet Mechanical-Mathematical Faculty of the M. V. Lomonosov Moscow State University. Official opponents: Academician A. N. Kolmogorov, Dr. of Physicomathematical Sciences D. V. Anosov, and Dr. of Physicomathematical Sciences Professor V. B. Lidskii.