Introduction to the Modern Theory of Dynamical Systems. Front Cover · Anatole Katok, Boris Hasselblatt. Cambridge University Press, – Mathematics – Dynamical Systems is the study of the long term behaviour of systems that A. Katok, B. Hasselblatt, Introduction to the modern theory of dynamical systems. Introduction to the modern theory of dynamical systems, by Anatole Katok and. Boris Hasselblatt, Encyclopedia of Mathematics and its Applications, vol.

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### Anatole Katok – Wikipedia

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. While in graduate school, Katok together with A. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms.

Katok’s collaboration with his former student Boris Hasselblatt resulted in the book Introduction to the Modern Theory of Dynamical Systemspublished by Cambridge University Press in Read, highlight, and take notes, across web, tablet, and phone. References to this book Dynamical Systems: This page was last edited on 17 Novemberat In he emigrated to the USA. Katok held tenured faculty positions at three mathematics departments: Modern Dynamical Systems and Applications.

His next result was the theory of monotone or Kakutani equivalence, which is based on a generalization of the concept of time-change in flows. 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. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The third and fourth parts develop in depth the theories of low-dimensional dynamical systems and hyperbolic dynamical systems.

Danville, PennsylvaniaU. Important contributions to ergodic theory and dynamical systems. 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. Stepin developed a theory of periodic approximations of measure-preserving transformations commonly known as Katok—Stepin approximations.

## Anatole Katok

Clark RobinsonClark Robinson No preview available – Mathematics ahsselblatt Dynamical Systems. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications.

Scientists and engineers working in applied dynamics, nonlinear science, and chaos will also find many fresh insights in this concrete and clear presentation. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. Retrieved dyynamical ” https: Views Read Edit View history.

Anatole KatokBoris Hasselblatt. Cambridge University Press- Mathematics – pages. In the last two decades Katok has been working on other rigidity phenomena, and in collaboration with several colleagues, made contributions to smooth rigidity and geometric rigidity, to differential and cohomological rigidity of smooth actions of higher-rank abelian groups and of lattices in Lie groups of higher rank, to measure rigidity for group actions and to nonuniformly hyperbolic actions of higher-rank abelian groups.

Liquid Mark A Miodownik Inbunden. It is one of the first rigidity statements hasselblztt dynamical systems. Inhe became a fellow of the American Mathematical Society. Introduction to the Modern Theory of Dynamical Systems. My library Help Advanced Book Search. 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.

### Introduction to the Modern Theory of Dynamical Systems

Katok became a member of American Academy of Arts and Sciences in Selected pages Title Page. His field of research was the theory of dynamical systems. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.