WorldCat Identities

Katok, A. B.

Overview
Works: 145 works in 435 publications in 3 languages and 6,622 library holdings
Genres: Conference papers and proceedings  Handbooks and manuals 
Roles: Author, Editor, Other, Honoree, Thesis advisor, Writer of accompanying material
Publication Timeline
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Most widely held works by A. B Katok
Handbook of dynamical systems by A. B Katok( )

26 editions published between 2002 and 2014 in English and held by 679 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
Introduction to the modern theory of dynamical systems by A. B Katok( Book )

21 editions published between 1995 and 2010 in English and Portuguese and held by 648 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
Rigidity in higher rank Abelian group actions by A. B Katok( )

24 editions published in 2011 in English and held by 641 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"--
Invariant manifolds, entropy, and billiards : smooth maps with singularities by A. B Katok( Book )

22 editions published between 1986 and 2008 in English and German and held by 577 WorldCat member libraries worldwide

A first course in dynamics : with a panorama of recent developments by Boris Hasselblatt( Book )

17 editions published between 2002 and 2010 in English and held by 426 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
Harmonic Maps, Conservation Laws and Moving Frames by Béla Bollobás( )

3 editions published in 2002 in English and held by 372 WorldCat member libraries worldwide

Annotation This accessible introduction to harmonic map theory and its analytical aspects, covers recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. It then presents a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A presentation of "exotic" functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a "Coulomb moving frame" is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces
Lectures on surfaces : (almost) everything you wanted to know about them by A. B Katok( Book )

16 editions published in 2008 in English and held by 368 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. At the same time, many of those notions appear in a technically simpler and more graphic form than in their general "natural" settings. The first, primarily expository, chapter introduces many of the principal actors -- the round sphere, flat torus, Möbius strip, Klein bottle, elliptic plane, etc.--as well as various methods of describing surfaces, beginning with the traditional representation by equations in three-dimensional space, proceeding to parametric representation, and also introducing the less intuitive, but central for our purposes, representation as factor spaces. It concludes with a preliminary discussion of the metric geometry of surfaces, and the associated isometry groups. Subsequent chapters introduce fundamental mathematical structures--topological, combinatorial (piecewise linear), smooth, Riemannian (metric), and complex--in the specific context of surfaces. The focal point of the book is the Euler characteristic, which appears in many different guises and ties together concepts from combinatorics, algebraic topology, Morse theory, ordinary differential equations, and Riemannian geometry. The repeated appearance of the Euler characteristic provides both a unifying theme and a powerful illustration of the notion of an invariant in all those theories. The assumed background is the standard calculus sequence, some linear algebra, and rudiments of ODE and real analysis. All notions are introduced and discussed, and virtually all results proved, based on this background."--Page 4 of cover
Typical dynamics of volume preserving homeomorphisms by Steve Alpern( )

3 editions published in 2001 in English and held by 356 WorldCat member libraries worldwide

This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley & ndash;Zehnder & ndash; Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property
Ergodic theory and dynamical systems : proceedings, special year, Maryland 1979-80( Book )

10 editions published between 1981 and 1982 in English and German and held by 351 WorldCat member libraries worldwide

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 )

14 editions published between 1999 and 2012 in English and held by 332 WorldCat member libraries worldwide

Combinatorial constructions in ergodic theory and dynamics by A. B Katok( Book )

9 editions published in 2003 in English and held by 226 WorldCat member libraries worldwide

"Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite and the notion of an individual point or an orbit makes no sense. Still there is a variety of situations when a measure-preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes)." "In the first part of this book this idea is developed systematically, genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type. The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales." "The book presents a view of ergodic theory not found in other expository sources and is suitable for graduate students familiar with measure theory and basic functional analysis."--BOOK JACKET
Handbook of dynamical systems( )

in English and held by 207 WorldCat member libraries worldwide

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to name just a few, are ubiquitous dynamical concepts throughout the articles
From groups to geometry and back by Vaughn Climenhaga( Book )

8 editions published in 2017 in English and held by 185 WorldCat member libraries worldwide

Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009
Ergodic theory and dynamical systems II : proceedings, special year, Maryland 1979-80 by Md.) University of Maryland (College Park( Book )

23 editions published between 1981 and 1982 in English and German and held by 144 WorldCat member libraries worldwide

Modern theory of dynamical systems : a tribute to Dmitry Victorovich Anosov( Book )

10 editions published between 2012 and 2017 in English and held by 125 WorldCat member libraries worldwide

This volume is a tribute to one of the founders of modern theory of dynamical systems, the late Dmitry Victorovich Anosov. It contains both original papers and surveys, written by some distinguished experts in dynamics, which are related to important themes of Anosov's work, as well as broadly interpreted further crucial developments in the theory of dynamical systems that followed Anosov's original work. Also included is an article by A. Katok that presents Anosov's scientific biography and a picture of the early development of hyperbolicity theory in its various incarnations, complete and partial, uniform and nonuniform
Introduction to the modern theory of dynamical systems by A. B Katok( Book )

26 editions published between 1995 and 2009 in English and Undetermined and held by 113 WorldCat member libraries worldwide

Introduction to the modern theory of dynamical systems by A. B Katok( Book )

18 editions published between 1995 and 2006 in English and held by 84 WorldCat member libraries worldwide

This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up
Ergodic theory and dynamical systems I : proceedings, special year, Maryland 1979-1980 by Special year in ergodic theory and dynamical systems( Book )

17 editions published between 1980 and 1981 in English and held by 80 WorldCat member libraries worldwide

Handbook of dynamical systems by Boris Hasselblatt( Book )

11 editions published between 2002 and 2006 in English and held by 37 WorldCat member libraries worldwide

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to name just a few, are ubiquitous dynamical concepts throughout the articles
Floer homology groups in Yang-Mills theory by S. K Donaldson( )

1 edition published in 2002 in English and held by 34 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 self-dual 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 Seiberg-Witten 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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WorldCat IdentitiesRelated Identities
Introduction to the modern theory of dynamical systems Introduction to the modern theory of dynamical systems Introduction to the modern theory of dynamical systems
Covers
Introduction to the modern theory of dynamical systemsRigidity in higher rank Abelian group actionsInvariant manifolds, entropy, and billiards : smooth maps with singularitiesA first course in dynamics : with a panorama of recent developmentsHarmonic Maps, Conservation Laws and Moving FramesLectures on surfaces : (almost) everything you wanted to know about themTypical dynamics of volume preserving homeomorphismsSmooth 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
Alternative Names
Anatole Katok Amerikaans wiskundige

Anatole Katok amerikansk matematikar

Anatole Katok amerikansk matematiker

Anatole Katok matematician american

Anatole Katok matemático ruso

Anatole Katok mathématicien américain

Anatole Katok US-amerikanischer Mathematiker

Katok, A.

Katok, A. 1944-

Katok, A. 1944-2018

Katok, A.B.

Katok, A. B. 1944-

Katok, A. B. 1944-2018

Katok, Anatole.

Katok, Anatole 1944-

Katok, Anatole B. 1944-

Katok, Anatole B. 1944-2018

Katok, Anatole Borisovich.

Katok, Anatoliĭ Borisovich

Katok, Anatoliĭ Borisovich, 1944-

Katok, Anatolij Borisovič 1944-

Katok, Anatolij Borisovič 1944-2018

Katok, Anatolij Borisovich 1944-

Katok, Anatolij Borisovich 1944-2018

Анатолій Борисович Каток Американський математик російського єврейського походження

Каток, Анатолий Борисович американский математик российского еврейского происхождения

Каток, Анатолий Борисович американский математик российского происхождения

安纳托利·卡托克 美国数学家

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