Anatole Katok
| Anatole Katok | |
|---|---|
 |
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| Native name | Анатолий Борисович Каток |
| Born |
August 9, 1944 Washington, DC – United States |
| Residence | United States |
| Nationality | United States |
| Fields | Mathematics – Dynamical Systems |
| Institutions | |
| Alma mater | Московский Государственный Университет |
| Doctoral advisor | Yakov Sinai |
| Doctoral students | Ralf J. Spatzier |
| Known for | Important contributions to ergodic theory and dynamical systems |
Anatole Borisovich Katok (Russian: Анатолий Борисович Каток; born August 9, 1944 in Washington DC) is an American mathematician with Russian origins. Katok is the Director of the Center for Dynamics and Geometry at the Pennsylvania State University. His field of research is the theory of dynamical systems.
Anatole Katok graduated from Moscow State University, from which he received his master's degree in 1965 and PhD in 1968 (with a thesis on "Applications of the Method of Approximation of Dynamical Systems by Periodic Transformations to Ergodic Theory" under Yakov Sinai). In 1978 he emigrated to the USA. He is married to the mathematician Svetlana Katok, who also works on dynamical systems and has been involved with Anatole Katok in the MASS Program for undergraduate students at Penn State.
While in graduate school, Katok (together with A. Stepin) developed a theory of periodic approximations of measure-preserving transformations commonly known as Katok—Stepin approximations. This theory helped to solve some problems that went back to von Neumann and Kolmogorov, and won the prize of the Moscow Mathematical Society in 1967.
His next result was the theory of monotone (or Kakutani) equivalence, which is based on a generalization of the concept of time-change in flows. There are constructions in the theory of dynamical systems that are due to Katok. Among these are the Anosov—Katok construction of smooth ergodic area-preserving diffeomorphisms of compact manifolds, the construction of Bernoulli diffeomorphisms with nonzero Lyapunov exponents on any surface, and the first construction of an invariant foliation for which Fubini's theorem fails in the worst possible way (Fubini foiled).
With Elon Lindenstrauss and Manfred Einsiedler, Katok made important progress on the Littlewood Conjecture in the theory of Diophantine approximations.
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