卡托克(Anatole Katok)作品集（共2卷） Collected Works Of Anatole Katok, The (In 2 Volumes)

基本信息

Format:Hardback 2696 pages

Publisher:World Scientific Publishing Co Pte Ltd

Imprint:World Scientific Publishing Co Pte Ltd

ISBN:9789811238062

Published:28 Aug 2023

Pub. Country:Singapore

页面参数仅供参考，具体以实物为准

书籍简介

♦ 这几卷书收集了 Anatole Katok 的大部分论文，他是现代动力系统理论的创始人之一。Katok 的工作反映了半个世纪的数学研究，包括遍历理论、双曲、椭圆和抛物线平滑动力学，以及高阶行动。他的论文涵盖了动力学中极其广泛的主题，其中包含了许多对后来的发展产生了巨大影响的开创性贡献，是公认的经典。

♦ 卷Ⅰ 的重点是： 双曲性、熵、测地流、区间交换变换、台球、扭曲图、光谱理论、近似、组合构造和动力学史。

♦ 卷2Ⅱ 的重点是： Cohomology和Geometric Rigidity，以及Measure Rigidity。

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papers which have already appeared in academic journals, this collection includes several previously unpublished papers as well as some whose English translation appears here for the first time.These collected works are organized by topic into six chapters, each featuring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 the 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, and Measure Rigidity.

作者简介

斯维特兰娜-卡托克 是宾夕法尼亚州立大学的数学教授。她的研究兴趣包括黎曼尼流形和对称空间的分析，双曲几何和富克斯群，遍历理论，符号动力学，以及动力系统在分析和数论中的应用。她还是2004年数学界妇女协会的Emmy Noether讲师，美国数学学会的研究员，Journal of Modern Dynamics的执行编辑，芝加哥大学出版社出版的Fuchsian Groups和美国数学学会出版的p-adic Analysis Compared with Real的作者。

巴萨姆-法亚德 是法国国家科学研究中心（CNRS）的研究主任，在Jussieu-Paris Rive Gauche的数学研究所任职。他的研究兴趣包括哈密尔顿动力学、KAM理论、Liouville现象和周期性近似的构造、抽象和平滑的遍历理论、同质动力学及其在Diophantine近似的应用。

Giovanni Forni 是马里兰大学的数学教授。他的研究兴趣包括Aubry-Mather理论、平滑抛物线流的遍历理论、Teichmüller动力学和应用于区间交换变换、翻译流和多边形的台球。他是2002年ICM关于ODE和动态系统部分的特邀发言人。2008年获得迈克尔-布林动态系统奖。自2012年起，他成为美国科学院院士。目前是《现代动力学杂志》的主编和迈克尔-布林动态系统奖委员会的领导。

鲍里斯-哈塞尔布拉特在加州理工学院获得博士学位，师从阿纳托尔-卡托克。他是数学教授，也是塔夫茨大学的前系主任和副教务长，担任过美国数学学会的第十一任秘书。研究集中在平滑的、以几何学为基础的、具有双曲行为的拓扑动力系统。

Mariusz Lemańczyk 在Nicolaus Copernicus 大学获得博士学位，是数学教授，曾任国立大学数学和计算机科学学院院长，现任动力学、数学分析和人工智能中心主任。他的研究重点是遍历理论及其与谱论和数论的相互作用。他是马赛CIRM担任Chaire Jean Morlet的仅有的波兰数学家。也是Studia Mathematica的编辑之一。

雅科夫-佩辛是宾夕法尼亚州立大学的数学教授。他的研究兴趣包括动态系统理论，重点是平滑遍历理论和热力学形式主义，黎曼几何学，动态学和分形几何学中的维度理论，统计和数学物理学。他还是欧洲学院（Academia Europea）的成员，自2012年起是美国数学学会的研究员，是Anatole Katok动态系统和几何学中心的主任。他在2009年获得UMALCA奖，在2015年获得Michael Brin动态系统奖。

Ralf Spatzier是密歇根大学安阿伯分校的数学教授，主要研究动态系统和遍历理论中的刚性问题，微分几何和李氏理论，特别是齐美尔计划，高等级非线性群的行动的刚性和黎曼几何中的高等级刚性现象。自2012年以来一直是美国科学院院士。目前在《现代动力学杂志》、《几何学专刊》和《密歇根数学杂志》的编委会任职。

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 Mathématiques 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 Supérieure. Giovanni Forni is Professor of Mathematics at the University of Maryland. His research interests include Aubry-Mather theory, ergodic theory of smooth parabolic flows, Teichmüller 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 Zürich 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.