Introduction to the Modern Theory of Dynamical Systems. Front Cover · Anatole Katok, Boris Hasselblatt. Cambridge University Press, – Mathematics – Introduction to the modern theory of dynamical systems, by Anatole Katok and. Boris Hasselblatt, Encyclopedia of Mathematics and its Applications, vol. Anatole Borisovich Katok was an American mathematician with Russian origins. Katok was the Katok’s collaboration with his former student Boris Hasselblatt resulted in the book Introduction to the Modern Theory of Dynamical Systems.

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Books by Boris Hasselblatt and Anatole Katok

Modern Dynamical Systems and Applications. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The final chapters introduce modern developments and applications of dynamics. Katok was also known for formulating conjectures and problems for some of which he even offered prizes that influenced bodies of work in dynamical systems.

Among these are the Hasselbblatt —Katok construction of smooth ergodic area-preserving diffeomorphisms of compact manifolds, the construction of Bernoulli diffeomorphisms with nonzero Lyapunov exponents on any surface, and the first construction of an invariant foliation for which Fubini’s theorem fails in the worst possible way Fubini foiled.


The best-known of these is the Katok Entropy Conjecture, which connects geometric and dynamical properties of geodesic flows. The third and fourth parts develop in depth the theories of low-dimensional dynamical systems and hyperbolic dynamical systems. Views Read Edit View history. Katok’s paradoxical example in measure theory”. Katok’s collaboration with his katko student Boris Hasselblatt resulted in the book Introduction to the Modern Theory of Dynamical Systemspublished by Cambridge University Press in The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity kattok the orbits structure.

Stepin developed a theory of periodic approximations of measure-preserving transformations commonly known as Katok—Stepin approximations. Anatole KatokBoris Hasselblatt. This theory helped to solve some problems that went back to von Neumann and Kolmogorovand won the prize of the Moscow Mathematical Society in Clark RobinsonClark Robinson No preview available – Mathematics — Dynamical Systems.

Anatole Katok

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. Account Options Sign in. It is one of the first rigidity statements in dynamical systems. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. It contains more than four hundred systematic exercises.

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. This page was last edited on 17 Novemberat Important contributions to ergodic theory and dynamical systems.


Hasselblatt and Katok

Introduction to the Modern Theory of Dynamical Systems. It includes density of periodic points and lower bounds on their number as well as exhaustion of topological entropy by horseshoes. Anatole Borisovich Katok Russian: The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. Selected pages Title Page. Katok became a member of American Academy of Arts and Sciences in From Wikipedia, the free encyclopedia.

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. In he emigrated to the USA.

His next result was the theory of monotone or Kakutani equivalence, which is based on a generalization of the concept of time-change ,atok flows. Shibley professorship since By using this site, you agree to the Terms of Use and Privacy Policy. Read, highlight, and take notes, across web, tablet, and phone. This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core kxtok discipline closely intertwined with most of the main areas of mathematics.