Oleksandr Mykolaiovych Sharkovsky

Olexandr Mikolajowytsch Scharkowski, Ukrainian Олександр Миколайович Шарковський, English transcription Oleksandr Mikolaiovich Sharkovsky or Sharkovskii, ( born December 7, 1936 in Kiev) is a Ukrainian mathematician who deals with dynamic systems.

Sharkovsky acquired in 1958 graduated from the Kiev State University and was in 1961 at the Institute of Mathematics of the Ukrainian Academy of Sciences in Kiev. He also taught from 1967 at the University of Kiev.

It deals with the theory of oscillations, stability theory of dynamical systems and theory of functional equations and difference equations.

He is known for the set of Scharkowski from 1964, among other things, with the result that discrete one-dimensional dynamical systems have with period 3 points with periods every other order. The sentence was rediscovered in 1975 by Li and James A. Yorke, and was one of the starting points of the resulting chaos theory in the 1970s.

His theorem is based on an arrangement of the natural numbers in order odd numbers ( 3,5,7 .... ), products of odd numbers with 2, then products with 4, 8, ..., with, .., and at the end of the powers of 2 in the reverse order ( ......, 4, 2, 1). It states that a discrete dynamical system on the real line, given by a continuous map f ( x), with a period n ( ie a point x with ) also has a period m with a following in the above arrangement, m. Especially for the period 3 implies that all natural numbers occur as periods. Has the dynamic system only finitely many periods, they must all be powers of 2.