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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
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Katok held tenured faculty positions at three mathematics departments: University of
Maryland (1978–1984), California Institute of Technology (1984–1990) and since 1990 at the Pennsylvania State University, where he held the Raymond N. Shibley professorship since 1996. He had advised 44 PhD students
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Katok's works on topological properties of nonuniformly hyperbolic dynamical systems. It includes density of periodic points and lower bounds on their number as well as exhaustion of topological entropy by horseshoes. These were the topic of his lecture at the
International Congress of Mathematicians
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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
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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
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191:; 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
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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
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and a member of the editorial boards of multiple other prestigious publications, including
Ergodic Theory and Dynamical Systems, Cambridge Tracts in Mathematics, and Cambridge Studies in Advanced Mathematics.
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207:, 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
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In 1967 Katok was awarded a Moscow
Mathematical Society for Young Mathematicians Prize (with A. Stepin and V. Oseledets). In 1983 he was an
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of higher rank, to measure rigidity for group actions and to nonuniformly hyperbolic actions of higher-rank abelian groups.
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Introduction to the Modern Theory of
Dynamical Systems, Encyclopedia of Mathematics and Its Applications 54
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on their thesis; the
Mathematics Genealogy Project lists most of his PhD students, and 121 descendants.
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Milnor, John. "John
Willard Milnor. Fubini foiled: Katok's paradoxical example in measure theory".
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Katok's emigration to the United States was prompted by anti-Jewish nature of Soviet
Communism.
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Pennsylvania State University, University Park, PA, University Lecture Series, 2003,
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Katok's collaboration with his former student Boris Hasselblatt resulted in the book
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on any surface, and the first construction of an invariant foliation for which
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628:"The work of Einsiedler, Katok and Lindenstrauss on the Littlewood conjecture"
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770:
211:). In 1978 he immigrated to the USA. He was married to the mathematician
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Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them
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Anatole Katok, mathematician who explored chaos theory, dies at 73
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A First Course in Dynamics with a Panorama of Recent Developments
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invited speaker at the International Congress of Mathematicians
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and Manfred Einsiedler, Katok made important progress on the
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Combinatorial Constructions in Ergodic Theory and Dynamics
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Brin, Michael; Hasselblatt, Boris; Pesin, Yakov (2004).
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Introduction to the Modern Theory of Dynamical Systems
590:. Cambridge University Press. pp. Introduction.
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List of Fellows of the American Mathematical Society
449:: Volume 1, Cambridge University Press, June 2011,
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259:fails in the worst possible way (Fubini foiled).
239:His next result was the theory of monotone (or
713:"Mathematics Genealogy Project-Anatole Katok"
632:Bulletin of the American Mathematical Society
446:Rigidity in Higher Rank Abelian Group Actions
432:, Pennsylvania State University – AMS, 2008,
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850:Fellows of the American Mathematical Society
845:University of Maryland, College Park faculty
759:Penn State Center for Dynamics and Geometry
543:"Center for Dynamical Systems and Geometry"
409:Anatole Katok and Boris Hasselblatt (eds.)
392:Anatole Katok and Boris Hasselblatt (eds.)
840:California Institute of Technology faculty
36:
18:
820:American people of Russian-Jewish descent
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587:Modern Dynamical Systems and Applications
308:Anatole Katok was Editor-in-Chief of the
780:Anatole Katok – Google Scholar Citations
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830:Pennsylvania State University faculty
754:Collection of Mathematical Interviews
426:Anatole Katok and Vaughn Climenhaga,
362:Boris Hasselblatt and Anatole Katok,
348:Anatole Katok and Boris Hasselblatt,
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815:21st-century American mathematicians
810:20th-century American mathematicians
660:"Anatole Katok's publication's list"
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366:Cambridge University Press, 2003,
352:Cambridge University Press, 1995,
296:University of California, Berkeley
149:California Institute of Technology
16:American mathematician (1944–2018)
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443:Anatole Katok and Viorel Nitica,
685:"Anatole Katok's Google Scholar"
835:Moscow State University alumni
1:
775:Mathematics Genealogy Project
645:10.1090/S0273-0979-07-01194-9
412:Handbook of Dynamical Systems
395:Handbook of Dynamical Systems
337:American Mathematical Society
290:in 1983, as well as the 1982
251:diffeomorphisms with nonzero
203:Anatole Katok graduated from
154:Pennsylvania State University
825:People from Washington, D.C.
729:Martin Weil (May 9, 2018), "
699:"Journal of Modern Dynamics"
855:Dynamical systems theorists
234:Moscow Mathematical Society
232:, and won the prize of the
99:Important contributions to
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487:"Anatole Katok's obituary"
310:Journal of Modern Dynamics
272:Diophantine approximations
414:, Vol 1B, Elsevier 2005,
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199:Early life and education
189:Анатолий Борисович Каток
181:Anatoly Borisovich Katok
30:Анатолий Борисович Каток
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398:Vol 1A, Elsevier 2002,
205:Moscow State University
139:Moscow State University
90:Moscow State University
326:Honors and recognition
78:Danville, Pennsylvania
626:A. Venkatesh (2008).
294:Memorial Lectures at
268:Littlewood conjecture
512:"Anatole Katok's CV"
736:The Washington Post
613:Math. Intelligencer
343:Selected monographs
282:and of lattices in
764:2014-07-14 at the
264:Elon Lindenstrauss
253:Lyapunov exponents
438:978-0-8218-4679-7
387:978-0-8218-3496-1
270:in the theory of
219:Work and research
193:dynamical systems
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126:dynamical systems
112:Scientific career
105:dynamical systems
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750:Eugene B. Dynkin
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164:Doctoral advisor
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805:2018 deaths
800:1944 births
638:: 117–134.
292:Rufus Bowen
226:von Neumann
209:Yakov Sinai
169:Yakov Sinai
122:Mathematics
794:Categories
670:2017-10-31
597:0521840732
553:2017-10-31
528:2017-10-31
462:References
372:0521587506
284:Lie groups
230:Kolmogorov
51:1944-08-09
249:Bernoulli
236:in 1967.
762:Archived
317:Teaching
241:Kakutani
773:at the
185:Russian
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245:Anosov
118:Fields
80:, U.S.
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522:(PDF)
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262:With
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228:and
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67:Died
45:Born
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
