Katok, A. B.
Most widely held works by A. B Katok
Introduction to the modern theory of dynamical systems by A. B Katok ( Book )
30 editions published between 1995 and 2006 in English and Portuguese and held by 569 libraries worldwide
This book provides 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 orbits structure. The third and fourth parts develop in depth the theories of low-dimensional dynamical systems and hyperbolic dynamical systems.
Invariant manifolds, entropy, and billiards : smooth maps with singularities by A. B Katok ( Book )
9 editions published between 1986 and 2008 in English and held by 381 libraries worldwide
Ergodic theory and dynamical systems : proceedings, special year, Maryland 1979-80 ( Book )
5 editions published in 1981 in English and German and held by 303 libraries worldwide
A first course in dynamics : with a panorama of recent developments by Boris Hasselblatt ( Book )
6 editions published between 2002 and 2003 in English and held by 301 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 )
3 editions published in 2008 in English and held by 265 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 )
1 edition published in 2001 in English and held by 247 libraries worldwide
Handbook of dynamical systems ( Book )
11 editions published between 2002 and 2005 in English and held by 211 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.
Modern dynamical systems and applications : dedicated to Anatole Katok on his 60th birthday ( Book )
2 editions published in 2004 in English and held by 182 libraries worldwide
Combinatorial constructions in ergodic theory and dynamics by A. B Katok ( Book )
4 editions published in 2003 in English and held by 180 libraries worldwide
Handbook of dynamical systems. Volume 1A ( Book )
4 editions published in 2002 in English and held by 94 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.
Rigidity in higher rank Abelian group actions by A. B Katok ( Book )
3 editions published in 2011 in English and held by 62 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"--Back Cover.
Handbook of dynamical systems. Volume 1B ( Book )
3 editions published in 2006 in English and held by 61 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 II : proceedings, special year, Maryland 1979-80 ( Book )
1 edition published in 1982 in English and held by 21 libraries worldwide
Handbook of dynamical systems. vol. 1B ( Book )
3 editions published in 2006 in English and held by 20 libraries worldwide
Handbook of dynamical systems. vol. 1A ( Book )
3 editions published in 2002 in English and held by 15 libraries worldwide
Dynamics, ergodic theory, and geometry dedicated to Anatole Katok ( Book )
1 edition published in 2007 in English and held by 14 libraries worldwide
Ergodic theory and dynamical systems. II Proceedings, special year, Maryland 1979-80 by Proceedings of ergodic theory and dynamical systems ( Book )
1 edition published in 1982 in English and held by 13 libraries worldwide
Rigidity in Higher Rank Abelian Group Actions, Volume 1 Introduction and Cocycle Problem by Anatole Katok ( Book )
3 editions published in 2011 in English and held by 10 libraries worldwide
Ideal for researchers in all aspects of dynamical systems and a useful introduction for graduate students entering the field.
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows by Steve Hurder ( Book )
3 editions published between 1990 and 1991 in English and held by 10 libraries worldwide
Publications mathematiques de l'IHES, 72 by Steve Hurder ( Book )
1 edition published in 1991 in French and held by 7 libraries worldwide
Abelian groups Characters of groups Combinatorial analysis Conference proceedings Differentiable dynamical systems Dynamics Entropy Ergodic theory Geodesic flows Geometry Global analysis (Mathematics) Handbooks, manuals, etc. Homotopy theory Invariant manifolds Katok, A. B Manifolds (Mathematics) Mathematics Rigidity (Geometry) Surfaces
Katok, A. 1944-
Katok, A. B.
Katok, A. B. 1944-
Katok, Anatoliĭ Borisovich
Katok, Anatolij Borisovič 1944-
Katok, Anatolij Borisovich 1944-