Ratner's Theorems on Unipotent Flows

Dave Witte Morris - Collection Chicago Lectures in Mathematics

204 pages, parution le 03/10/2005

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Résumé

The theorems of Berkeley mathematician Marina Ratner have guided key advances in the understanding of dynamical systems. Unipotent flows are well-behaved dynamical systems, and Ratner has shown that the closure of every orbit for such a flow is of a simple algebraic or geometric form. In Ratner's Theorems on Unipotent Flows, Dave Witte Morris provides both an elementary introduction to these theorems and an account of the proof of Ratner's measure classification theorem.

A collection of lecture notes aimed at graduate students, the first four chapters of Ratner's Theorems on Unipotent Flows can be read independently. The first chapter, intended for a fairly general audience, provides an introduction with examples that illustrate the theorems, some of their applications, and the main ideas involved in the proof. In the following chapters, Morris introduces entropy, ergodic theory, and the theory of algebraic groups. The book concludes with a proof of the measure-theoretic version of Ratner's Theorem. With new material that has never before been published in book form, Ratner's Theorems on Unipotent Flows helps bring these important theorems to a broader mathematical readership.

Sommaire

Introduction to Ratner's theorems
Introduction to entropy
Facts from ergodic theory
Facts about algebraic groups
Proof of the measure-classification theorem

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	PAPIER
Éditeur(s)	The University of Chicago Press
Auteur(s)	Dave Witte Morris
Collection	Chicago Lectures in Mathematics
Parution	03/10/2005
Nb. de pages	204
Format	15,5 x 23
Couverture	Broché
Poids	340g
Intérieur	Noir et Blanc
EAN13	9780226539843
ISBN13	978-0-226-53984-3