Yakov G. Sinai
Yakov Grigorevich Sinai (Russian: Я́ков Григо́рьевич Сина́й; born September 21, 1935) is a mathematician known for his work on dynamical systems. He contributed to the modern metric theory of dynamical systems and connected the world of deterministic (dynamical) systems with the world of probabilistic (stochastic) systems. He has also worked on mathematical physics and probability theory. His efforts have provided the groundwork for advances in the physical sciences.
Sinai has won several awards, including the Nemmers Prize, the Wolf Prize in Mathematics and the Abel Prize.
Yakov Grigorevich Sinai was born into a Russian Jewish academic family on September 21, 1935, in Moscow, Soviet Union (now Russia). His parents, Nadezda Kagan and Gregory Sinai, were both microbiologists. His grandfather, Veniamin Kagan, headed the Department of Differential Geometry at Moscow State University and was a major influence on Sinai's life.
Sinai received his bachelor's and master's degrees from Moscow State University. In 1960, he earned his Ph.D., also from Moscow State; his adviser was Andrey Kolmogorov. Together with Kolmogorov, he showed that even for "unpredictable" dynamic systems, the level of unpredictability of motion can be described mathematically. In their idea, which became known as Kolmogorov–Sinai entropy, a system with zero entropy is entirely predictable, while a system with non-zero entropy has an unpredictability factor directly related to the amount of entropy.
In 1963, Sinai introduced the idea of dynamical billiards, also known as "Sinai Billiards". In this idealized system, a particle bounces around inside a square boundary without loss of energy. Inside the square is a circular wall, of which the particle also bounces off. He then proved that for most initial trajectories of the ball, this system is ergodic, that is, after a long time, the amount of that time the ball will have spent in any given region on the surface of the table is approximately proportional to the area of that region. It was the first time anyone proved a dynamic system was ergodic.
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