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Ratner's Theorems on Unipotent Flows

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Ratner's Theorems on Unipotent Flows Cover

 

Synopses & Reviews

Publisher Comments:


The theorems of Berkeley mathematician Marina Ratner have guided key advances in the undertanding 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 faily 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.

About the Author

Dave Witte Morris is professor of mathematics at the University of Lethbridge.

Table of Contents

1. Introduction to Ratner's theorems

2. Introduction to entropy

3. Facts from ergodic theory

4. Facts about algebraic groups

5. Proof of the measure-classification theorem

Product Details

ISBN:
9780226539843
Author:
Morris, Dave Witte
Publisher:
University Of Chicago Press
Subject:
Calculus
Subject:
Number Theory
Subject:
Advanced
Subject:
Algebra - Abstract
Subject:
Lie groups
Subject:
Measure theory
Subject:
Mathematics-Calculus
Copyright:
Edition Description:
Paperback
Series:
Chicago Lectures in Mathematics
Publication Date:
August 2005
Binding:
Paperback
Grade Level:
Professional and scholarly
Language:
English
Pages:
203
Dimensions:
9 x 6 in

Related Subjects

Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Dynamics

Ratner's Theorems on Unipotent Flows New Trade Paper
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Product details 203 pages University of Chicago Press - English 9780226539843 Reviews:
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