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Oleksandr Sharkovsky
Олександр Шарковський
Sharkovsky in 2006
Born	(1936-12-07)7 December 1936 Kyiv, Ukrainian SSR, Soviet Union
Died	21 November 2022(2022-11-21) (aged 85) Kyiv, Ukraine
Nationality	Ukrainian
Other names	O.M. Sharkovskyi, O.M. Sharkovskii, O.M. Sharkovskyy, O.M. Šarkovskii, O.M. Sharkovs’kyi
Citizenship	Soviet Union (1936-1991) Ukraine (1991-2022)
Alma mater	Taras Shevchenko National University of Kyiv
Known for	Sharkovsky's theorem
Scientific career
Fields	Mathematics, Dynamical systems, Differential and difference equations, Mathematical physics, Topology
Institutions	Institute of Mathematics of the National Academy of Sciences of Ukraine
Thesis	Some questions in the theory of one-dimensional iterative processes  (1961)
Doctoral advisor	Yurii Mitropolskiy
Doctoral students	Iryna Sushko
Website	imath.kiev.ua/~asharkov/

Oleksandr Mykolayovych Sharkovsky (Ukrainian: Олекса́ндр Миколайович Шарко́вський; 7 December 1936 – 21 November 2022) was a Soviet and Ukrainian mathematician most famous for developing Sharkovsky's theorem on the periods of discrete dynamical systems 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 (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", 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 he successfully completed postgraduate studies at the NASU Institute of Mathematics 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 National Academy of Sciences of Ukraine. 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. 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 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 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 theorem, Sharkovsky's ordering, Sharkovsky's space, Sharkovsky's stratification, etc.

Sharkovsky's theorem 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" — 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 "Russian Mathematical Surveys", (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 for a series of papers "Complex dynamic finite-dimensional and infinite-dimensional systems" (2005)
• State Prize of Ukraine in Science and Technology 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

1. also Sharkovskyi, Sharkovskyy, Sharkovs’kyi, sometimes Šarkovskii or Sarkovskii

References

1. imath.kiev.ua/~asharkov/
2. Alexander Sharkovsky, Mathematics genealogy.
3. ^ "Uspekhi Matematicheskikh Nauk (eng. "Russian Mathematical Surveys"), 7, 1952" (PDF).
4. ^ "Sharkovsky O.M. - Institute of Mathematics, NAS of Ukraine". imath.kiev.ua. Retrieved 2023-01-19.
5. "Sharkovsky, Oleksandr". Institute of Mathematics. Retrieved June 29, 2013.
6. O'Connor, J. J.; Robertson, E. F. "Oleksandr Mikolaiovich Sharkovsky biography". University of St. Andrews. Archived from the original on November 9, 2019.
7. "Шарковський Олександр Миколайович - Інститут математики НАН України". imath.kiev.ua. Retrieved 2023-01-19.
8. "Oleksandr Mykolayovych Sharkovsky (07.12.1936 – 21.11.2022)". imath. 22 November 2022. Retrieved 22 November 2022.
9. Sharkovsky, A. N.; Kolyada, S. F.; Sivak, A. G.; Fedorenko, V. V. (1997). Dynamics of One-Dimensional Maps. doi:10.1007/978-94-015-8897-3. ISBN 978-90-481-4846-2.
10. Sharkovsky, Aleksandr Nikolayevich (2008-05-12). "Sharkovsky ordering". Scholarpedia. 3 (5): 1680. Bibcode:2008SchpJ...3.1680S. doi:10.4249/scholarpedia.1680. ISSN 1941-6016.
11. ^ Sharkovsky, A.N. (November 2019). "Sharkovsky ordering and combinatorial dynamics" (PDF).
12. Sharkovsky, A.; Romanenko, E.; Berezovsky, S. (August 2003). "Ideal turbulence: Definition and models". 2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775). Vol. 1. pp. 23–30 vol.1. doi:10.1109/PHYCON.2003.1236779. ISBN 0-7803-7939-X. S2CID 122863918.
13. Sharkovsky, A. N. (2006-06-01). "Ideal Turbulence". Nonlinear Dynamics. 44 (1): 15–27. doi:10.1007/s11071-006-1931-7. ISSN 1573-269X. S2CID 195068450.
14. Sharkovs’kyi, О. М. (2022). "Дескриптивна теорія детермінованого хаосу". Ukrains'kyi Matematychnyi Zhurnal (in Ukrainian). 74 (12): 1709–1718. doi:10.37863/umzh.v74i12.6515. ISSN 1027-3190. S2CID 256155036.
15. Sharkovsky, O. M. (2023-05-01). "Descriptive Theory of Deterministic Chaos". Ukrainian Mathematical Journal. 74 (12): 1950–1960. doi:10.1007/s11253-023-02180-z. ISSN 1573-9376.

External links

• Sharkovsky Oleksandr Mykolayovych memorial page at the Institute of Mathematics NAS of Ukraine (in Ukrainian)
• Oleksandr Sharkovsky at the Mathematics Genealogy Project
• Oleksandr Mikolaiovich Sharkovsky at the MacTutor History of Mathematics archive (in Ukrainian)

v t e Chaos theory
Concepts	Core Attractor Bifurcation Fractal Limit set Lyapunov exponent Orbit Periodic point Phase space Anosov diffeomorphism Arnold tongue axiom A dynamical system Bifurcation diagram Box-counting dimension Correlation dimension Conservative system Ergodicity False nearest neighbors Hausdorff dimension Invariant measure Lyapunov stability Measure-preserving dynamical system Mixing Poincaré section Recurrence plot SRB measure Stable manifold Topological conjugacy Theorems Ergodic theorem Liouville's theorem Krylov–Bogolyubov theorem Poincaré–Bendixson theorem Poincaré recurrence theorem Stable manifold theorem Takens's theorem
Theoretical branches	Bifurcation theory Control of chaos Dynamical system Ergodic theory Quantum chaos Stability theory Synchronization of chaos
Chaotic maps (list)	Discrete Arnold's cat map Baker's map Complex quadratic map Coupled map lattice Duffing map Dyadic transformation Dynamical billiards outer Exponential map Gauss map Gingerbreadman map Hénon map Horseshoe map Ikeda map Interval exchange map Irrational rotation Kaplan–Yorke map Langton's ant Logistic map Standard map Tent map Tinkerbell map Zaslavskii map Continuous Double scroll attractor Duffing equation Lorenz system Lotka–Volterra equations Mackey–Glass equations Rabinovich–Fabrikant equations Rössler attractor Three-body problem Van der Pol oscillator
Physical systems	Chua's circuit Convection Double pendulum Elastic pendulum FPUT problem Hénon–Heiles system Kicked rotator Multiscroll attractor Population dynamics Swinging Atwood's machine Tilt-A-Whirl Weather
Chaos theorists	Michael Berry Rufus Bowen Mary Cartwright Chen Guanrong Leon O. Chua Mitchell Feigenbaum Peter Grassberger Celso Grebogi Martin Gutzwiller Brosl Hasslacher Michel Hénon Svetlana Jitomirskaya Bryna Kra Edward Norton Lorenz Aleksandr Lyapunov Benoît Mandelbrot Hee Oh Edward Ott Henri Poincaré Itamar Procaccia Mary Rees Otto Rössler David Ruelle Caroline Series Yakov Sinai Oleksandr Mykolayovych Sharkovsky Nina Snaith Floris Takens Audrey Terras Mary Tsingou Marcelo Viana Amie Wilkinson James A. Yorke Lai-Sang Young
Related articles	Butterfly effect Complexity Edge of chaos Predictability Santa Fe Institute

• 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