Anatole Katok

Anatoly Borisovich Katok (; August 9, 1944 – April 30, 2018) was an American mathematician with Russian-Jewish origins. Katok was the director of the Center for Dynamics and Geometry at the Pennsylvania State University. His field of research was the theory of dynamical systems.

Early life and education 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 immigrated to the USA. He was married to the mathematician Svetlana Katok, who also works on dynamical systems and has been involved with Katok in the MASS Program for undergraduate students at Penn State.

Katok was also known for formulating conjectures and problems (for some of which he even offered prizes) that influenced bodies of work in dynamical systems. The best-known of these is the Katok Entropy Conjecture, which connects geometric and dynamical properties of geodesic flows. It is one of the first rigidity statements in dynamical systems. In the last two decades Katok has been working on other rigidity phenomena, and in collaboration with several colleagues, made contributions to smooth rigidity and geometric rigidity, to differential and cohomological rigidity of smooth actions of higher-rank abelian groups and of lattices in Lie groups of higher rank, to measure rigidity for group actions and to nonuniformly hyperbolic actions of higher-rank abelian groups.

Honors and recognition In 1967 Katok was awarded a Moscow Mathematical Society for Young Mathematicians Prize (with A. Stepin and V. Oseledets). In 1983 he was an invited speaker at the International Congress of Mathematicians in Warsaw (his talk was titled "Nonuniform hyperbolicity and structure of smooth dynamical systems"). Katok became a member of American Academy of Arts and Sciences in 2004. In 2012, he became a fellow of the American Mathematical Society.

Selected monographs Anatole Katok and Boris Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and Its Applications 54 Cambridge University Press, 1995, Boris Hasselblatt and Anatole Katok, A First Course in Dynamics with a Panorama of Recent Developments Cambridge University Press, 2003. Anatole Katok, Combinatorial Constructions in Ergodic Theory and Dynamics Pennsylvania State University, University Park, Pennsylvania, University Lecture Series, 2003. Anatole Katok and Boris Hasselblatt (eds.) Handbook of Dynamical Systems Vol 1A, Elsevier 2002. Anatole Katok and Boris Hasselblatt (eds.) Handbook of Dynamical Systems, Vol 1B, Elsevier 2005. Anatole Katok and Vaughn Climenhaga, Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them, Pennsylvania State University – AMS, 2008. Anatole Katok and Viorel Nitica, Rigidity in Higher Rank Abelian Group Actions: Volume 1, Cambridge University Press, June 2011.