WorldCat Identities

Katok, A. B.

Overview
Works: 99 works in 303 publications in 3 languages and 4,062 library holdings
Genres: Conference proceedings  Handbooks, manuals, etc 
Roles: Editor, Other, Honoree, Thesis advisor, Writer of accompanying material
Classifications: QA614.8, 530.1435
Publication Timeline
Key
Publications about  A. B Katok Publications about A. B Katok
Publications by  A. B Katok Publications by A. B Katok
Most widely held works by A. B Katok
Introduction to the modern theory of dynamical systems by A. B Katok ( Book )
52 editions published between 1995 and 2009 in English and held by 743 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
Invariant manifolds, entropy, and billiards : smooth maps with singularities by A. B Katok ( Book )
15 editions published between 1986 and 2008 in English and German and held by 477 WorldCat member libraries worldwide
Handbook of dynamical systems by Boris Hasselblatt ( )
27 editions published between 2002 and 2006 in English and held by 421 WorldCat member libraries worldwide
This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey Principal Structures of Volume 1A. The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations). . Written by experts in the field. . The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems
Ergodic theory and dynamical systems : proceedings, special year, Maryland 1979-80 by Md.) University of Maryland (College Park ( Book )
16 editions published between 1981 and 1982 in English and German and held by 378 WorldCat member libraries worldwide
A first course in dynamics : with a panorama of recent developments by Boris Hasselblatt ( Book )
12 editions published between 2002 and 2003 in English and held by 335 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
Lectures on surfaces : (almost) everything you wanted to know about them by A. B Katok ( Book )
9 editions published in 2008 in English and held by 296 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
Smooth ergodic theory and its applications : proceedings of the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications, July 26-August 13, 1999, University of Washington, Seattle by AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications ( Book )
9 editions published in 2001 in English and held by 270 WorldCat member libraries worldwide
Handbook of dynamical systems ( )
20 editions published between 2002 and 2006 in English and held by 246 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 cross-references 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
Combinatorial constructions in ergodic theory and dynamics by A. B Katok ( Book )
6 editions published in 2003 in English and held by 194 WorldCat member libraries worldwide
Rigidity in higher rank Abelian group actions by A. B Katok ( Book )
5 editions published in 2011 in English and held by 143 WorldCat member libraries worldwide
"This self-contained 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"--
Rigidity in Higher Rank Abelian Group Actions, Volume 1 Introduction and Cocycle Problem by A. B Katok ( )
5 editions published in 2011 in English and held by 48 WorldCat member libraries worldwide
Ideal for researchers in all aspects of dynamical systems and a useful introduction for graduate students entering the field
Rigidity in higher rank Abelian group actions by A. B Katok ( )
9 editions published in 2011 in English and held by 34 WorldCat member libraries worldwide
"In a very general sense modern theory of smooth dynamical systems deals with smooth actions of "sufficiently large but not too large" groups or semigroups (usually locally compact but not compact) on a "sufficiently small" phase space (usually compact, or, sometimes, finite volume manifolds). Important branches of dynamics specifically consider actions preserving a geometric structure with an infinite-dimensional group of automorphisms, two principal examples being a volume and a symplectic structure. The natural equivalence relation for actions is differentiable (corr. volume preserving or symplectic) conjugacy"--
Typical dynamics of volume preserving homeomorphisms by Steve Alpern ( )
3 editions published in 2001 in English and held by 22 WorldCat member libraries worldwide
This book provides a self-contained introduction to typical properties of volume preserving homeomorphisms. Stress is given to the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. An excellent introduction for newcomers, and an indispensable resource for experts
Dynamics, ergodic theory, and geometry dedicated to Anatole Katok ( Book )
2 editions published in 2007 in English and held by 19 WorldCat member libraries worldwide
Ergodic theory and dynamical systems I : proceedings, special year, Maryland 1979-1980 ( Book )
2 editions published in 1981 in English and held by 19 WorldCat member libraries worldwide
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows by Steve Hurder ( Book )
5 editions published between 1990 and 1991 in English and French and held by 16 WorldCat member libraries worldwide
Modern dynamical systems and applications : dedicated to Anatole Katok on his 60th birthday ( Book )
2 editions published in 2004 in English and held by 14 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)
Floer homology groups in Yang-Mills theory by S. K Donaldson ( )
2 editions published in 2002 in English and held by 14 WorldCat member libraries worldwide
The seminal work of Floer has now been placed in a contemporary setting. The author of this monograph writes with the big picture constantly in mind, reviewing current knowledge and predicting future directions. This forms part of the work for which Simon Donaldson was awarded the prestigious Fields Medal
Introduction and cocycle problem by A. B Katok ( )
2 editions published in 2011 in English and held by 13 WorldCat member libraries worldwide
Ergodic theory and dynamical systems : proceedings, special year, Maryland 1979-80 ( Book )
2 editions published in 1981 in Undetermined and English and held by 13 WorldCat member libraries worldwide
 
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Audience level: 0.73 (from 0.33 for Ergodic th ... to 0.90 for Combinator ...)
Alternative Names
Katok, A.
Katok, A. 1944-
Katok, A.B.
Katok, A. B., 1944-
Katok, Anatole.
Katok, Anatole, 1944-
Katok, Anatole B. 1944-
Katok, Anatoliĭ Borisovich
Katok, Anatolij Borisovič, 1944-
Katok, Anatolij Borisovich 1944-
Languages
English (201)
German (3)
French (1)
Covers