Oleksandr Scharkowskyj

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Sharkovsky

Oleksandr Mykolajowytsch Scharkowskyj ( Ukrainian Олександр Миколайович Шарковський , English transcription Oleksandr Mikolaiovich Sharkovsky or Sharkovskii * 7. December 1936 in Kiev , Ukrainian SSR ) is a Ukrainian mathematician who deals with dynamic systems.

Life

Scharkowskyj graduated from the Kiev State University in 1958 and was from 1961 at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR in Kiev. From 1967 he also taught at the University of Kiev. Since 2006 he has been an academician of the National Academy of Sciences of Ukraine, where he is the head of the Institute of Mathematics, whose team was awarded the 2010 State Prize of Ukraine in Science and Technology.

plant

He deals with the theory of vibrations, the stability theory of dynamic systems and the theory of functional equations and difference equations.

He is known for the Scharkowskyj theorem from 1964, which among other things has the consequence that discrete one-dimensional dynamic systems with period 3 points with periods of every other order. The sentence was rediscovered in 1975 by Li and James A. Yorke and was one of the starting points of the chaos theory that emerged in the 1970s .

His theorem is based on an arrangement of the natural numbers in the order odd numbers (3,5,7 ...), products of the odd numbers with 2, then products with 4, with 8, ..., with , .., and at the end the powers of 2 in reverse order (... ..., 4, 2, 1). It says that a discrete dynamical system on the real number line, given by a continuous mapping f (x), with a period n (i.e. a point x with ) also has a period m with a subsequent m in the above arrangement. Especially for period 3 it follows that all natural numbers occur as periods. If the dynamic system only has finitely many periods, all of these must be powers of 2.

Web links

Individual evidence

  1. ↑ Sometimes just Sarkovskii
  2. ↑ Profile Oleksandr Scharkowskyj ( Memento of the original from June 30, 2016 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. on the website of the National Academy of Sciences of Ukraine; accessed on April 2, 2017 (Ukrainian) @1@ 2Template: Webachiv / IABot / www.nas.gov.ua
  3. ↑ Biography of Oleksandr Scharkowskyj ; accessed on April 2, 2017 (Ukrainian)
  4. ↑ AN Sarkovskii, Coexistence of Cycles of a Continuous Mapping of a Line on Itself (Russian), Ukr. Mat. Z., 16, 1964, 61
personal data
SURNAME Scharkowskyj, Oleksandr
ALTERNATIVE NAMES Scharkowskyj, Oleksandr Mykolajowytsch (full name); Шарковський, Олександр Миколайович (Ukrainian); Sharkovsky, Oleksandr Mikolaiovich (English)
BRIEF DESCRIPTION Ukrainian mathematician
DATE OF BIRTH December 7, 1936
PLACE OF BIRTH Kiev , Ukrainian SSR