Pesin and Ya. Sinai Ergodic Theory and Dynamical Systems / Volume 2 / Issue. The following statement plays an important role in the study of ergodic. Of Sinai’s theory culminated in a solution, in some form, of a classical hy- pothesis by L. Boltzmann (stated back in the 1880’s) on the ergodicity of gases of hard balls.

Contents • • • • Biography [ ] Yakov Grigorevich Sinai was born into a academic family on September 21, 1935, in Moscow, (now Russia). His parents, Nadezda Kagan and Gregory Sinai, were both microbiologists. His grandfather,, headed the Department of Differential Geometry at 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. 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, 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, 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, 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. Also in 1963, Sinai announced a proof of the for a gas consisting of n hard spheres confined to a box. The complete proof, however, was never published, and in 1987 Sinai declared that the announcement was premature. The problem remains open to this day.

From 1960 to 1971, Sinai was a researcher in the Laboratory of Probabilistic and Statistical Methods at Moscow State University. In 1971 he accepted a position as senior researcher at the in Russia, while continuing to teach at Moscow State. He had to wait until 1981 to become a professor at Moscow State, likely because he had supported the dissident poet, mathematician and human rights activist in 1968. Since 1993, Sinai has been a professor of mathematics at, while maintaining his position at the Landau Institute.

For the 1997–98 academic year, he was the Thomas Jones Professor at Princeton, and in 2005, the Moore Distinguished Scholar at the. In 2002, Sinai won the for his 'revolutionizing' work on dynamical systems, statistical mechanics, probability theory, and statistical physics. In 2005, the dedicated an issue to Sinai writing 'Yakov Sinai is one of the greatest mathematicians of our time.

His exceptional scientific enthusiasm inspire[d] several generations of scientists all over the world.' In 2013, Sinai received the for Lifetime Achievement. In 2014, the awarded him the, for his contributions to dynamical systems,, and mathematical physics. Presenting the award, said Sinai had solved real world physical problems 'with the soul of a mathematician'. He praised the tools developed by Sinai which demonstrate how systems that look different may in fact have fundamental similarities. The prize comes with 6 million, equivalent at the time to $US 1 million or £600,000. He was also inducted into the Norwegian Academy of Science and Letters.

Other awards won by Sinai include the (1986), the (1990), the (1992), the (1997), the (2008) and the (2009). He is a member of the United States, the, and the. He is an honorary member of the and, in 2012, he became a fellow of the. Sinai has been selected an honorary member of the, the, the, and the of London. He holds honorary degrees from the, the,, and. Sinai has authored more than 250 papers and books. Concepts in mathematics named after him include Sinai's random walk, Sinai–Ruelle–Bowen measures, and Pirogov–Sinai theory.

Sinai has overseen more than 50 Ph. Psy Trance Loops Samples. D. He has spoken at the four times. In 2000, he was a plenary speaker at the First Latin American Congress in Mathematics. Sinai is married to mathematician and physicist Elena B. The couple have written several joint papers. Selected works [ ] • Introduction to Ergodic Theory. Princeton 1976.

• Topics in Ergodic Theory. Princeton 1977, 1994. • Probability Theory – an Introductory Course. Springer, 1992. • Theory of probability and Random Processes (with Koralov).

2nd edition, Springer, 2007. • Theory of Phase Transitions – Rigorous Results.

Pergamon, Oxford 1982. • Ergodic Theory (with Isaac Kornfeld and ).

Springer, Grundlehren der mathematischen Wissenschaften 1982. •, Notices AMS 2004. • in Bulletin AMS. Adaanaa Font. • 'How mathematicians and physicists found each other in the theory of dynamical systems and in statistical mechanics', in Mathematical Events of the Twentieth Century (editors: Bolibruch, Osipov, & Sinai). Springer 2006, p. Flash Banner Creator 2.10 Crack.  399.