Katok, A. B.
Overview
Works:  124 works in 407 publications in 3 languages and 5,641 library holdings 

Genres:  Conference papers and proceedings Handbooks and manuals 
Roles:  Author, Editor, Other, Honoree, Thesis advisor, Writer of accompanying material 
Classifications:  QA614.8, 515.352 
Publication Timeline
.
Most widely held works about
A. B Katok
Most widely held works by
A. B Katok
Introduction to the modern theory of dynamical systems by
A. B Katok(
Book
)
57 editions published between 1995 and 2010 in English and held by 755 WorldCat member libraries worldwide
The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. Scientists and engineers working in applied dynamics, nonlinear science, and chaos will also find many fresh insights in this concrete and clear presentation. It contains more than four hundred systematic exercises
57 editions published between 1995 and 2010 in English and held by 755 WorldCat member libraries worldwide
The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. Scientists and engineers working in applied dynamics, nonlinear science, and chaos will also find many fresh insights in this concrete and clear presentation. It contains more than four hundred systematic exercises
A first course in dynamics : with a panorama of recent developments by
Boris Hasselblatt(
Book
)
15 editions published between 2002 and 2010 in English and held by 379 WorldCat member libraries worldwide
"The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course
15 editions published between 2002 and 2010 in English and held by 379 WorldCat member libraries worldwide
"The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course
Invariant manifolds, entropy, and billiards : smooth maps with singularities by
A. B Katok(
Book
)
20 editions published between 1986 and 2008 in 3 languages and held by 374 WorldCat member libraries worldwide
20 editions published between 1986 and 2008 in 3 languages and held by 374 WorldCat member libraries worldwide
Lectures on surfaces : (almost) everything you wanted to know about them by
A. B Katok(
Book
)
13 editions published in 2008 in English and held by 309 WorldCat member libraries worldwide
Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors  the round sphere, flat torus, Mobius strip, and Klein bottle
13 editions published in 2008 in English and held by 309 WorldCat member libraries worldwide
Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors  the round sphere, flat torus, Mobius strip, and Klein bottle
Handbook of dynamical systems by
Boris Hasselblatt(
Book
)
46 editions published between 2002 and 2006 in English and held by 296 WorldCat member libraries worldwide
Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample crossreferences between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005
46 editions published between 2002 and 2006 in English and held by 296 WorldCat member libraries worldwide
Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample crossreferences between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005
Smooth ergodic theory and its applications : proceedings of the AMS Summer Research Institute on Smooth Ergodic Theory and
Its Applications, July 26August 13, 1999, University of Washington, Seattle by AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications(
Book
)
13 editions published between 1999 and 2001 in English and held by 285 WorldCat member libraries worldwide
13 editions published between 1999 and 2001 in English and held by 285 WorldCat member libraries worldwide
Combinatorial constructions in ergodic theory and dynamics by
A. B Katok(
Book
)
8 editions published in 2003 in English and held by 204 WorldCat member libraries worldwide
8 editions published in 2003 in English and held by 204 WorldCat member libraries worldwide
Rigidity in higher rank Abelian group actions by
A. B Katok(
Book
)
25 editions published in 2011 in English and held by 177 WorldCat member libraries worldwide
"This selfcontained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems"
25 editions published in 2011 in English and held by 177 WorldCat member libraries worldwide
"This selfcontained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems"
Ergodic theory and dynamical systems II : proceedings, special year, Maryland 197980 by
Md.) University of Maryland (College Park(
Book
)
38 editions published between 1981 and 1982 in 3 languages and held by 151 WorldCat member libraries worldwide
38 editions published between 1981 and 1982 in 3 languages and held by 151 WorldCat member libraries worldwide
From groups to geometry and back by
Vaughn Climenhaga(
Book
)
3 editions published in 2017 in English and held by 33 WorldCat member libraries worldwide
3 editions published in 2017 in English and held by 33 WorldCat member libraries worldwide
Dynamics, ergodic theory, and geometry by
Boris Hasselblatt(
Book
)
6 editions published in 2007 in English and held by 30 WorldCat member libraries worldwide
This volume contains surveys and research articles by leading experts in several areas of dynamical systems that have recently experienced substantial progress. Some of the major surveys focus on symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; and ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this a fascinating look at the state of the art
6 editions published in 2007 in English and held by 30 WorldCat member libraries worldwide
This volume contains surveys and research articles by leading experts in several areas of dynamical systems that have recently experienced substantial progress. Some of the major surveys focus on symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; and ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this a fascinating look at the state of the art
Handbook of dynamical systems Volume 1A(
)
1 edition published in 2002 in English and held by 23 WorldCat member libraries worldwide
Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample crossreferences between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005
1 edition published in 2002 in English and held by 23 WorldCat member libraries worldwide
Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample crossreferences between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005
Modern dynamical systems and applications : dedicated to Anatole Katok on his 60th birthday(
Book
)
2 editions published in 2004 in English and held by 16 WorldCat member libraries worldwide
This volume presents a wide cross section of current research in the theory of dynamical systems and contains articles by leading researchers, including several Fields medalists, in a variety of specialties. These are surveys, usually with new results included, as well as research papers that are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, applications. The target audience includes dynamicists, who will find new results in their own specialty as well as surveys in others, and mathematicians from other disciplines who look for a sample of current developments in ergodic theory and dynamical systems. (Midwest)
2 editions published in 2004 in English and held by 16 WorldCat member libraries worldwide
This volume presents a wide cross section of current research in the theory of dynamical systems and contains articles by leading researchers, including several Fields medalists, in a variety of specialties. These are surveys, usually with new results included, as well as research papers that are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, applications. The target audience includes dynamicists, who will find new results in their own specialty as well as surveys in others, and mathematicians from other disciplines who look for a sample of current developments in ergodic theory and dynamical systems. (Midwest)
Differentiability, rigidity and GodbillonVey classes for Anosov flows by
Steve Hurder(
Book
)
5 editions published between 1990 and 1991 in English and French and held by 15 WorldCat member libraries worldwide
5 editions published between 1990 and 1991 in English and French and held by 15 WorldCat member libraries worldwide
Lectures on surfaces (almost) everything you wanted to know about them by
A. B Katok(
Book
)
1 edition published in 2008 in English and held by 15 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 15 WorldCat member libraries worldwide
Introduction and cocycle problem by
A. B Katok(
)
2 editions published in 2011 in English and held by 1 WorldCat member library worldwide
2 editions published in 2011 in English and held by 1 WorldCat member library worldwide
Set theory by
George J Tourlakis(
)
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
This twovolume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a userfriendly conversational lecture style that makes them equally effective for selfstudy or class use. Volume II, on formal (ZFC) set theory, incorporates a selfcontained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
This twovolume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a userfriendly conversational lecture style that makes them equally effective for selfstudy or class use. Volume II, on formal (ZFC) set theory, incorporates a selfcontained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing
Harmonic Maps, Conservation Laws and Moving Frames by
Béla Bollobás(
)
2 editions published in 2002 in English and held by 0 WorldCat member libraries worldwide
An accessible and selfcontained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book will be of particular interest to graduate students and researchers in geometry, analysis of partial differential equations and mathematical physics
2 editions published in 2002 in English and held by 0 WorldCat member libraries worldwide
An accessible and selfcontained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book will be of particular interest to graduate students and researchers in geometry, analysis of partial differential equations and mathematical physics
Floer Homology Groups in YangMills Theory by
S. K Donaldson(
)
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
Annotation This monograph gives a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The material contained here was developed with specific applications in mind. However, it has now become clear that the techniques used are important for many current areas of research. An important example would be symplectic theory and gluing problems for selfdual metrics and other metrics with special holonomy. The author writes with the big picture constantly in mind. As well as a review of the current state of knowledge, there are sections on the likely direction of future research. Included in this are connections between Floer groups and the celebrated SeibergWitten invariants. The results described in this volume form part of the area known as Donaldson theory. The significance of this work is such that the author was awarded the prestigious Fields Medal for his contribution
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
Annotation This monograph gives a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The material contained here was developed with specific applications in mind. However, it has now become clear that the techniques used are important for many current areas of research. An important example would be symplectic theory and gluing problems for selfdual metrics and other metrics with special holonomy. The author writes with the big picture constantly in mind. As well as a review of the current state of knowledge, there are sections on the likely direction of future research. Included in this are connections between Floer groups and the celebrated SeibergWitten invariants. The results described in this volume form part of the area known as Donaldson theory. The significance of this work is such that the author was awarded the prestigious Fields Medal for his contribution
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Related Identities
 Hasselblatt, Boris Other Author Editor
 Fulton, W. Other Editor
 Bollobas, B. Other Editor
 Sarnak, P. Other Editor
 Kirwan, F. Other Editor
 Strelcyn, JeanMarie Author
 Climenhaga, Vaughn 1982 Author
 American Mathematical Society Publisher
 Nițica, Viorel Other
 Pesin, Ya. B. Editor
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Associated Subjects
Abelian groups Cell aggregationMathematics Combinatorial analysis Differentiable dynamical systems Dynamics Entropy Ergodic theory Geometry Geometry, Differential Global analysis (Mathematics) Group actions (Mathematics) Group theory Harmonic maps Invariant manifolds Katok, A. B Logic, Symbolic and mathematical Mathematical analysis Mathematics Number theory Riemannian manifolds Rigidity (Geometry) Set theory Surfaces Topology YangMills theory
Alternative Names
Anatole Katok Amerikaans wiskundige
Anatole Katok amerikansk matematikar
Anatole Katok amerikansk matematiker
Anatole Katok matemático ruso
Anatole Katok mathématicien américain
Anatole Katok USamerikanischer Mathematiker
Katok, A.
Katok, A. 1944
Katok, A.B.
Katok, A. B. 1944
Katok, Anatole.
Katok, Anatole 1944
Katok, Anatole B. 1944
Katok, Anatole Borisovich.
Katok, Anatoliĭ Borisovich
Katok, Anatolij Borisovič 1944
Katok, Anatolij Borisovich 1944
Каток, Анатолий Борисович американский математик российского происхождения
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