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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Anatole Borisovich Katok Russian: His field of research was the theory of dynamical systems. In he emigrated to the USA.
Books by Boris Hasselblatt and Anatole Katok
While in graduate school, Katok together with A. Stepin developed a theory of periodic approximations of measure-preserving transformations commonly known as Katok—Stepin approximations.
This theory helped to solve some problems that went back to von Neumann and Kolmogorovand won the prize of the Moscow Mathematical Society in 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. There are constructions in the theory of dynamical systems that are due to Katok. Among these are the Anosov —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.
With Elon Lindenstrauss and Manfred Einsiedler, Katok made important progress on the Littlewood conjecture in the theory of Diophantine approximations.
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. The best-known kstok these is the Katok Entropy Conjecture, which connects geometric and dynamical properties of geodesic flows. It is one of the first rigidity statements in dynamical systems. 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 hasselhlatt, 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.
First Course in Dynamics – E-bok – Boris Hasselblatt, Anatole Katok () | Bokus
Katok’s works on topological properties of nonuniformly hyperbolic dynamical systems. It includes density of periodic points and lower bounds on their number as well as exhaustion of topological entropy by horseshoes. 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 This book is considered as encyclopedia of modern dynamical systems and is among the most cited kato, in the area.
Katok held tenured faculty positions at three mathematics departments: Shibley professorship since Katok became a member of American Academy of Arts and Sciences in Inhe became a fellow of the American Mathematical Society. From Wikipedia, the free encyclopedia. Danville, PennsylvaniaU. Modern Dynamical Systems and Applications.
Hasselblatt and Katok
Important contributions to ergodic theory and dynamical systems.
Mathematics — Dynamical Systems.