In 1952, Sharkovsky's name appeared in the mathematical world - the magazine "Russian Mathematical Surveys",[3] 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).[4] Soon thereafter, in 1967,[4] he defended his doctoral thesis. In 1978,[4] 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.
Oleksandr Sharkovsky created the foundations of the topological theory of one-dimensional dynamic systems,[9] 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.
Research conducted by O. M. Sharkovsky allowed him to propose the concept of "ideal turbulence"[12][13] — 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.[4] O. M. Sharkovsky is the author of almost 250 scientific works,[4] including five monographs written in co-authorship with students. Among the students are 3 doctors and 14 candidates of sciences.[4]
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.[4] 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).[4]
His last paper "Descriptive theory of determined chaos"[14] was published in the Ukrains’kyi Matematychnyi Zhurnal (Ukrainian Mathematical Journal) in January 2023 and translated in July 2023 with publication in Springer Link.[15]
Awards and prizes
The first prize of the Kyiv Olympiad of Young Mathematicians (1951), the magazine "Russian Mathematical Surveys",[3] (UMS, 7, 1952)