These volumes collect most of the papers of Anatole Katok, one of the founders of the modern theory of dynamical systems. Katok's work reflects half a century of research in mathematics and includes ergodic theory, hyperbolic, elliptic, and parabolic smooth dynamics, as well as higher-rank actions. Katok's papers cover an extremely broad range of topics in dynamics, and they contain many seminal contributions that had great impact on later developments and are now widely recognized as classical.Katok also authored numerous historical and biographical papers, and these contain accounts of crucial developments from the point of view of one of the main protagonists.Besides papers which have already appeared in academic journals, this collection includes several previously unpublished papers as well as some whose English translation appears here for the first time.These collected works are organized by topic into six chapters, each featuring an introduction written by respective leading specialists. Volume I focuses on following topics: Hyperbolicity, Entropy, Geodesic Flows, Interval Exchange Transformations, Billiards, Twist Maps, Spectral Theory, Approximations, Combinatorial Constructions, and History of Dynamics. Volume II focuses on these topics: Cohomology and Geometric Rigidity, Measure Rigidity.

� propos de l?auteur

Svetlana Katok is Professor of Mathematics at the Pennsylvania State University. Her research interests include analysis on Riemannian manifolds and symmetric spaces, hyperbolic geometry and Fuchsian groups, ergodic theory, symbolic dynamics, and application of dynamical systems to analysis and number theory. She was the 2004 Emmy Noether Lecturer of the Association for Women in Mathematics. She is a fellow of American Mathematical Society since 2012 (Inaugural Class). She is managing editor of Journal of Modern Dynamics and the author of Fuchsian Groups, published by University of Chicago Press, and p-adic Analysis Compared with Real published by the American Mathematical Society. Bassam Fayad is a Research Director at the Centre National de Recherche Scientifique (CNRS) in France, Institut de Math�matiques de Jussieu-Paris Rive Gauche. His research interests include Hamiltonian dynamics, KAM theory, Liouville phenomena and constructions by periodic approximations, abstract and smooth ergodic theory, homogeneous dynamics and their applications to Diophantine approximations. He was an invited speaker at the ICM in 2018 in the Section on ODE's and Dynamical Systems. He is editor in the Tunisian Journal of Mathematics and in the Annales de l'Ecole Normale Sup�rieure. Giovanni Forni is Professor of Mathematics at the University of Maryland. His research interests include Aubry-Mather theory, ergodic theory of smooth parabolic flows, Teichm�ller dynamics and applications to Interval Exchange Transformations, Translation flows and Billiards in Polygons. He was an invited speaker at the ICM in 2002 in the Section on ODE's and Dynamical Systems. In 2008 he was the recipient of the first Michael Brin Prize in Dynamical Systems. He has been a Fellow of the AMS since 2012 (Inaugural Class). He is currently Editor in Chief of the Journal of Modern Dynamics and Chair of the Committee of the Michael Brin Prize in Dynamical Systems. Boris Hasselblatt obtained his doctorate at Caltech under the guidance of Anatole Katok. He is a professor of mathematics as well as former department chair and Associate Provost at Tufts University. His research centers on smooth, geometrically motivated, and topological dynamical systems with hyperbolic behavior. He has coauthored the books Introduction to the Modern Theory of Dynamical Systems, Dynamics: A first course | with a panorama of recent developments (both with Cambridge University Press) and Hyperbolic Flows (with the European Mathematical Society) and edited six other books. He is a Fellow of the American Mathematical Society and one of only two Americans to hold the Chaire Jean Morlet at CIRM in Marseille. His recent full-semester visiting professorships include the ETH Z�rich and the University of Tokyo. He cofounded the Journal of Modern Dynamics, Electronic Research Announcements – Mathematical Sciences, and Mathematics Research Reports, and he serves as the eleventh Secretary of the American Mathematical Society. Mariusz Lemańczyk obtained his doctorate at Nicolaus Copernicus University (NCU) and his habilitation at Warsaw University. He is a professor of mathematics, a former dean of the Faculty of Mathematics and Computer Science of NCU and the present director of the Excellence Center "Dynamics, Mathematical Analysis and Artificial Intelligence". His research focuses on ergodic theory and its interactions with spectral theory and number theory. He authored and coauthored about 120 research articles, one monograph on the spectral theory from the ergodic theory point of view and coedited one book Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics (series Lecture Notes). He is a recipient of Banach prize and Kuratowski prize. He is the only Polish mathematician to hold the Chaire Jean Morlet at CIRM in Marseille. His recent visiting professorships include Auckland University, Bielefeld University, Hebrew University of Jerusalem, Institute for Advanced Studies (Princeton), Institute for Low Temperature in Kharkov, Ohio State University (Columbus), Penn State University, University of Aix-Marseille, University of Geneva, University of Normandie, Tel Aviv University. He is one of editors of Studia Mathematica. Yakov Pesin is Distinguished Professor of Mathematics at the Pennsylvania State University. His research interest includes the theory of dynamical systems with focus on smooth ergodic theory and thermodynamic formalism, Riemannian geometry, dimension theory in dynamics and fractal geometry, statistical and mathematical physics. Yakov Pesin is a member of European Academy (Academia Europea) and a fellow of the American Mathematical Society since 2012 (Inaugural Class). He is also Director of Anatole Katok Center for Dynamical Systems and Geometry. He was an invited speaker at the International Congress of Mathematicians in 1986 in the Section on ODE's and Dynamical Systems. He (co-)authored 6 books, and co-edited 7 books and he is a member of the editorial board of the journal Ergodic Theory and Dynamical Systems. Federico Rodriguez Hertz received his training in mathematics from IMPA, Brazil. He holds the Anatole Katok Chair Professorship at The Pennsylvania State University. His main research interests are in Ergodic Theory and Dynamical Systems, especially for smooth systems and more general group actions and its connection with rigidity phenomena. He was invited speaker at the ICM in 2010 in Hyderabad, India in the Dynamical Systems and Ordinary Differential Equations Section. He received the UMALCA prize in 2009 and the Michael Brin Prize in Dynamical Systems in 2015. Ralf Spatzier is Professor of Mathematics at the University of Michigan, Ann Arbor. He primarily works on rigidity problems in dynamical systems and ergodic theory, differential geometry and Lie theory, especially the Zimmer program, rigidity of actions of higher rank abelian groups and higher rank rigidity phenomena in Riemannian geometry. He has been a Fellow of the AMS since 2012 (Inaugural Class). He currently serves on the editorial boards of the Journal of Modern Dynamics, Geometriae Dedicata and the Michigan Mathematics Journal.

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