Katok, A. B.
Overview
Works:  65 works in 264 publications in 3 languages and 4,214 library holdings 

Genres:  Conference proceedings Handbooks, manuals, etc 
Roles:  Author, Editor, Honoree, Thesis advisor, Other, 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
Handbook of dynamical systems by
Boris Hasselblatt(
)
48 editions published between 2002 and 2014 in English and held by 820 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 infinitedimensional 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
48 editions published between 2002 and 2014 in English and held by 820 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 infinitedimensional 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
Introduction to the modern theory of dynamical systems by
A. B Katok(
Book
)
53 editions published between 1995 and 2009 in English and held by 774 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
53 editions published between 1995 and 2009 in English and held by 774 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 498 WorldCat member libraries worldwide
15 editions published between 1986 and 2008 in English and German and held by 498 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 359 WorldCat member libraries worldwide
The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAMtheory."pub. desc
12 editions published between 2002 and 2003 in English and held by 359 WorldCat member libraries worldwide
The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAMtheory."pub. desc
Ergodic theory and dynamical systems : proceedings, special year, Maryland 197980(
Book
)
12 editions published between 1981 and 1982 in English and German and held by 327 WorldCat member libraries worldwide
12 editions published between 1981 and 1982 in English and German and held by 327 WorldCat member libraries worldwide
Lectures on surfaces : (almost) everything you wanted to know about them by
A. B Katok(
Book
)
10 editions published in 2008 in English and held by 295 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
10 editions published in 2008 in English and held by 295 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 26August 13, 1999, University of Washington, Seattle by AMS Summer Research Institute on Smooth Ergodic Theory and its Applications(
Book
)
11 editions published in 2001 in English and held by 286 WorldCat member libraries worldwide
11 editions published in 2001 in English and held by 286 WorldCat member libraries worldwide
Combinatorial constructions in ergodic theory and dynamics by
A. B Katok(
Book
)
6 editions published in 2003 in English and held by 197 WorldCat member libraries worldwide
6 editions published in 2003 in English and held by 197 WorldCat member libraries worldwide
Rigidity in higher rank Abelian group actions by
A. B Katok(
Book
)
16 editions published in 2011 in English and held by 193 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 infinitedimensional 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"
16 editions published in 2011 in English and held by 193 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 infinitedimensional 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"
Ergodic theory and dynamical systems II : proceedings, special year, Maryland 197980 by Proceedings of ergodic theory and dynamical systems(
Book
)
6 editions published in 1982 in English and held by 61 WorldCat member libraries worldwide
6 editions published in 1982 in English and held by 61 WorldCat member libraries worldwide
Rigidity in Higher Rank Abelian Group Actions, Volume 1 Introduction and Cocycle Problem by
A. B Katok(
)
2 editions published in 2011 in English and held by 30 WorldCat member libraries worldwide
Ideal for researchers in all aspects of dynamical systems and a useful introduction for graduate students entering the field
2 editions published in 2011 in English and held by 30 WorldCat member libraries worldwide
Ideal for researchers in all aspects of dynamical systems and a useful introduction for graduate students entering the field
Dynamics, ergodic theory, and geometry dedicated to Anatole Katok(
Book
)
5 editions published in 2007 in English and held by 26 WorldCat member libraries worldwide
5 editions published in 2007 in English and held by 26 WorldCat member libraries worldwide
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
Introduction and cocycle problem by
A. B Katok(
)
2 editions published in 2011 in English and held by 15 WorldCat member libraries worldwide
2 editions published in 2011 in English and held by 15 WorldCat member libraries worldwide
Differentiability, rigidity and GodbillonVey classes for Anosov flows by
Steve Hurder(
Book
)
4 editions published between 1990 and 1991 in English and French and held by 15 WorldCat member libraries worldwide
4 editions published between 1990 and 1991 in English and French and held by 15 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 13 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 13 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)
Ergodic theory and dynamical systems : proceedings, special year, Maryland 197980(
Book
)
2 editions published in 1981 in Undetermined and English and held by 13 WorldCat member libraries worldwide
2 editions published in 1981 in Undetermined and English and held by 13 WorldCat member libraries worldwide
Ergodic theory and dynamical systems : proceedings, special year, Maryland 1979  80 by
Md.) University of Maryland (College Park(
Book
)
1 edition published in 1982 in German and held by 12 WorldCat member libraries worldwide
1 edition published in 1982 in German and held by 12 WorldCat member libraries worldwide
Ergodic theory and dynamical systems : proceedings by
A. B Katok(
Book
)
3 editions published in 1981 in English and held by 6 WorldCat member libraries worldwide
3 editions published in 1981 in English and held by 6 WorldCat member libraries worldwide
Publications mathematiques de l'IHES by
Steve Hurder(
Book
)
1 edition published in 1991 in French and held by 6 WorldCat member libraries worldwide
1 edition published in 1991 in French and held by 6 WorldCat member libraries worldwide
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