astronomy

Oleksandr Sharkovsky

Oleksandr Sharkovsky is a astronomy topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Oleksandr Sharkovsky rather than just read about it. In short: Oleksandr Mykolayovych Sharkovsky (Ukrainian: Олекса́ндр Миколайович Шарко́вський; 7 December 1936 – 21 November 2022) was a 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).

Key takeaways

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Reference excerpt

Oleksandr Mykolayovych Sharkovsky (Ukrainian: Олекса́ндр Миколайович Шарко́вський; 7 December 1936 – 21 November 2022) was a 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. 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

References

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)

Illustrations

Worked examples

Example 1 — a first encounter with Oleksandr Sharkovsky

Start with the simplest possible case. Write down what Oleksandr Sharkovsky claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Oleksandr Sharkovsky before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Oleksandr Sharkovsky ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Oleksandr Sharkovsky

In research: Oleksandr Sharkovsky appears in astronomy research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Oleksandr Sharkovsky in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Oleksandr Sharkovsky is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1936 births, 2022 deaths, Academic staff of the Taras Shevchenko National University of Kyiv, so understanding it makes those chapters shorter.
In everyday life: Look for Oleksandr Sharkovsky outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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Frequently asked questions

What is Oleksandr Sharkovsky in simple terms?

Why does Oleksandr Sharkovsky matter?

Because it connects several astronomy ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Oleksandr Sharkovsky?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Oleksandr Sharkovsky.