◀ ▲ ▶History / 20th-century / Person: Sharkovsky, Oleksandr Mikolaiovich
Person: Sharkovsky, Oleksandr Mikolaiovich
Oleksandr Sharkovsky was a Ukrainian mathematician who made contributions to the theory of discrete dynamical systems.
Mathematical Profile (Excerpt):
- Sharkovsky's main areas of interest are the theory of dynamical systems, the theory of stability and the theory of oscillations.
- He published this result, known today as Sharkovsky's Theorem, in the Russian paper Co-existence of cycles of a continuous mapping of the line into itself (1964).
- Although the result did not attract a great deal of interest at the time of its publication, during the 1970s other surprising results were proved which turned out to be special cases of Sharkovsky's theorem.
- The Sharkovsky theorem led to the appearance of numerous works in this direction, where one can often encounter terms such as the Sharkovsky theorem, Sharkovsky order, Sharkovsky space, Sharkovsky set, Sharkovsky stratification, and maximum period in the sense of Sharkovsky.
- Around the same time Sharkovsky published papers (some written in Russian, some in Ukrainian) such as: Fixed points and the center of a continuous mapping of the line into itself (1964), On cycles and the structure of a continuous mapping (1965), On attracting and attracted sets (1965), Continuous mapping on a set of w-limit points (1965), and A classification of fixed points (1965).
- Sharkovsky obtained fundamental results in the general theory of dynamical systems on arbitrary compact sets.
- Sharkovsky also described types of global stability for almost all dynamical systems and established exact descriptive bounds for sets consisting of trajectories with different asymptotics.
- Sharkovsky has, in collaboration with others, written a number of important monographs.
- In 1986, in collaboration with Yu L Maistrenko and E Yu Romanenko, Sharkovsky published the Russian monograph Difference equations and their applications.
- Sharkovsky, in collaboration with S F Kolyada, A G Sivak and V V Fedorenko, published Dynamics of one-dimensional mappings in 1989.
- In 1978, Sharkovsky was elected as a corresponding member of the USSR Academy of Sciences.
- In 1994, an international conference "Thirty years after Sharkovsky's theorem.
- The papers show how much influence on the development of the theory of dynamical systems that Sharkovsky's results have had and continue to have.
- The meeting served to summarize the progress made since Professor Sharkovsky's discovery, and to explore new directions.
- Thirty-seven papers were delivered at the conference and included in the proceedings, including the talk Universal phenomena in some boundary value problems by Sharkovsky himself.
- The Proceedings included an English translation of Sharkovsky's famous 1964 paper Coexistence of cycles of a continuous map of the line into itself.
- The results in the theory of dynamical systems obtained in the 1960s by Sharkovsky appeared to be very important when the necessity for a general investigation of essentially nonlinear processes arose.
- It turned out that many fundamental results and ideas of the contemporary theory of dynamical systems can be found in the early works of Sharkovsky.
- Without any doubt, recent investigations of Sharkovsky into the mathematical aspects of nonlinear dynamics and, in particular, in the theory of turbulent oscillations will occupy with time an important place in various branches of science related to nonlinear processes.
Born 7 December 1936, Kiev, Ukranian SSR (now Kyiv, Ukraine). Died 21 November 2022.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive