Oleksandr Mykolayovych Sharkovsky (; 7 December 1936 – 21 November 2022) was a Ukrainian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

most famous for developing

Sharkovsky's theorem In mathematics, Sharkovskii's theorem (also spelled Sharkovsky, Sharkovskiy, Šarkovskii or Sarkovskii), named after Oleksandr Mykolayovych Sharkovsky, who published it in 1964, is a result about discrete dynamical systems. One of the implications ...

on the periods of

discrete dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock ...

s in 1964. He was a corresponding member of the Academy of Sciences of the Ukrainian SSR (1978), and academician of the

National Academy of Sciences of Ukraine The National Academy of Sciences of Ukraine (NASU; , ; ''NAN Ukrainy'') is a self-governing state-funded organization in Ukraine that is the main center of development of Science and technology in Ukraine, science and technology by coordinatin ...

(2006). Prize laureate of the National Academy of Sciences of Ukraine named after M. M. Bogolyubov and M. O. Lavretiev.

Life and career

In 1952, Sharkovsky's name appeared in the mathematical world - the magazine "

Russian Mathematical Surveys ''Uspekhi Matematicheskikh Nauk'' () is a Russian mathematical journal, published by the Russian Academy of Sciences and Moscow Mathematical Society and translated into English as ''Russian Mathematical Surveys''. ''Uspekhi Matematicheskikh Nauk' ...

", when eighth-grader Oleksandr Sharkovsky became the winner of the Kyiv Mathematical Olympiad for schoolchildren. By his first year in Kyiv National University, he had already written his first scientific work. After graduating with honors from

Taras Shevchenko National University of Kyiv The Taras Shevchenko National University of Kyiv (; also known as Kyiv University, Shevchenko University, or KNU) is a public university in Kyiv, Ukraine. The university is the third-oldest university in Ukraine after the University of Lviv and ...

he successfully completed postgraduate studies at the

NASU Institute of Mathematics The Institute of Mathematics of the National Academy of Sciences of Ukraine () is a government-owned research institute in Ukraine that carries out basic research and trains highly qualified professionals in the field of mathematics. It was founded ...

with an early defense of his candidate's thesis (1961). Soon thereafter, in 1967, he defended his doctoral thesis. In 1978, O. M. Sharkovsky was elected a corresponding member of the Academy of Sciences of the Ukrainian SSR. Since 1974, O. M. Sharkovsky headed the department of differential equations of the Institute of Mathematics of the Ukrainian SSR Academy of Sciences, and since 1986 he headed the department of the theory of dynamical systems, which was created on his initiative. In 2006, Sharkovsky became a full member of the

. He is the head of the department of the Theory of dynamical systems at the

Institute of Mathematics of the National Academy of Sciences of Ukraine The Institute of Mathematics of the National Academy of Sciences of Ukraine () is a government-owned research institute in Ukraine that carries out basic research and trains highly qualified professionals in the field of mathematics. It was founded ...

. In the last years of his life, he worked as a chief researcher of the Department of Theory of Dynamic Systems and Fractal Analysis of the Institute of Mathematics of the National Academy of Sciences. O.M. Sharkovsky died on 21 November 2022, at the age of 85 in the

Feofaniya Clinical Hospital Feofaniya Clinical Hospital () is a hospital of State Management of Affairs of Ukraine which designated to provide medical service to Ukrainian officials. It is located on the southern outskirts of Kyiv next to village of Novosilky of Fastiv Raio ...

in Kyiv.

Scientific work

Oleksandr Sharkovsky created the foundations of the topological theory of one-dimensional dynamic systems, a theory that today is one of the tools for researching evolutionary problems of the most diverse nature. He discovered the law of coexistence of periodic trajectories of different periods; the topological structure of basins of attraction of various sets is investigated; a number of criteria of simplicity and complexity of dynamic systems were obtained. O. M. Sharkovsky also contributed fundamental results in

dynamical systems theory Dynamical systems theory is an area of mathematics used to describe the behavior of complex systems, complex dynamical systems, usually by employing differential equations by nature of the ergodic theory, ergodicity of dynamic systems. When differ ...

on arbitrary topological spaces. The achievements of the Ukrainian scientist received general recognition in international scientific circles. The formation and development of chaotic dynamics are associated with his name. In the scientific literature, you can find such terms as

, Sharkovsky's ordering, Sharkovsky's space, Sharkovsky's stratification, etc.

is associated with initiating a new direction in the theory of dynamical systems — combinatorial dynamics. In 1994, an international conference "Thirty years of Sharkovsky's theorem" was held in Spain. New perspectives". Research conducted by O. M. Sharkovsky allowed him to propose the concept of "

ideal turbulence Ideal may refer to: Philosophy * Ideal (ethics), values that one actively pursues as goals * Platonic ideal, a philosophical idea of trueness of form, associated with Plato Mathematics * Ideal (ring theory), special subsets of a ring considere ...

" — a new mathematical phenomenon in deterministic systems that models the most complex properties of turbulence in time and space, namely: the processes of the formation of coherent structures of decreasing scales and the birth of random states. O. M. Sharkovsky actively combines scientific work with pedagogical activity. From the mid-60s of the 20th century. gave general courses and lectures on the theory of dynamic systems at the mechanical and mathematical faculty of his native university. O. M. Sharkovsky is the author of almost 250 scientific works, including five monographs written in co-authorship with students. Among the students are 3 doctors and 14 candidates of sciences. The Ukrainian scientist devoted a lot of energy and time to developing scientific relations. He gave lectures at universities and scientific centers in more than 20 countries in Europe and America, and at universities in China and Australia. He was a member of the editorial boards of a number of international mathematical publications, in particular, he was a co-editor of the journal "Journal of Difference Equations and Applications" (USA). His last paper "Descriptive theory of determined chaos" was published in the Ukrains’kyi Matematychnyi Zhurnal (Ukrainian Mathematical Journal) in January 2023 and translated in July 2023 with publication in Springer Link.

Awards and prizes

* The first prize of the Kyiv Olympiad of Young Mathematicians (1951), the magazine "

", (UMS, 7, 1952) * The Bogoliubov Prize of National Academy of Sciences of Ukraine for the series of works "The theory of scattering of quantum systems and one-dimensional dynamical systems" (1993) *

The Lavrentyev Prize of National Academy of Sciences of Ukraine ''The'' is a grammatical article in English, denoting nouns that are already or about to be mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in English. ''The' ...

for a series of papers "Complex dynamic finite-dimensional and infinite-dimensional systems" (2005) *

State Prize of Ukraine in Science and Technology State most commonly refers to: * State (polity), a centralized political organization that regulates law and society within a territory **Sovereign state, a sovereign polity in international law, commonly referred to as a country **Nation state, a ...

for the cycle of scientific works "Theory of dynamic systems: modern methods and their application" (2010) * Bernd Aulbach Prize of the International Society of Difference Equations (2011) * Honorary doctorate Doctor Honoris Causa (Dr. h. c.) from the Silesian University in Opava, Czech Republic (2014) * The Mitropolskiy Prize of National Academy of Sciences of Ukraine, Kyiv (2019)

Notes

References

External links

Sharkovsky Oleksandr Mykolayovych memorial page
at the Institute of Mathematics NAS of Ukraine *
Oleksandr Mikolaiovich Sharkovsky
at the MacTutor History of Mathematics archive {{DEFAULTSORT:Sharkovsky, Oleksandr 1936 births 2022 deaths Scientists from Kyiv Ukrainian mathematicians Full Members of the National Academy of Sciences of Ukraine Taras Shevchenko National University of Kyiv alumni Academic staff of the Taras Shevchenko National University of Kyiv