History of Science and Engineering Annotation << Back Whether is Newton’s mechanic finished? Kolmogorov–Arnold–Mozer theory R.R. Mukhin This article is devoted to the fundamental A.N.Kolmogorov’s achievement in classical mechanics. The development of concepts of classical dynamical equations is discussed. Evolution of these concepts from always integrable to nonintegrable systems and also the origin of «the principal problem» of dynamics are shown. The solution of «the principal problem» in KAM-theory is elucidated. The special attention to Kolmogorov’s contribution in the creation of this theory is given. The influence on the formation of modern point of view on nonintegrable systems and application of KAM-theory in understanding of nature are considered. Key words: Newton mechanics; dynamical system; perturbation theory; nonintegriability; instability; KAM-theory. E-mail: moi@pstu.ac.ru