Dave Witte Morris's Books

Ratner's Theorems on Unipotent Flows

By: Dave Witte Morris

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Ratner's Theorems on Unipotent Flows

By: Dave Witte Morris

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.

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Page Count

224

Publisher

University of Chicago Press

Published Date

ISBN 10

0226539830

ISBN 13

9780226539836

Ratner's Theorems on Unipotent Flows

By: Dave Witte Morris

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Ratner's Theorems on Unipotent Flows

By: Dave Witte Morris

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Page Count

216

Publisher

University of Chicago Press

Published Date

ISBN 10

0226539849

ISBN 13

9780226539843

Ergodic Theory, Groups, and Geometry

NSF-CBMS Regional Research Conferences in the Mathematical Sciences, June 22-26, 1998, University of Minnesota

By: Robert J. Zimmer,Dave Witte Morris

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Ergodic Theory, Groups, and Geometry

NSF-CBMS Regional Research Conferences in the Mathematical Sciences, June 22-26, 1998, University of Minnesota

By: Robert J. Zimmer,Dave Witte Morris

The study of group actions on manifolds is the meeting ground of a variety of mathematical areas. In particular, interesting geometric insights can be obtained by applying measure-theoretic techniques. This book provides an introduction to some of the important methods, major developments, and open problems in the subject. It is slightly expanded from lectures given by Zimmer at the CBMS conference at the University of Minnesota. The main text presents a perspective on the field as it was at that time. Comments at the end of each chapter provide selected suggestions for further reading, including references to recent developments."--BOOK JACKET.

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Page Count

103

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821883364

ISBN 13

9780821883365

Introduction to Arithmetic Groups

By: Dave Witte Morris

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Introduction to Arithmetic Groups

By: Dave Witte Morris

This book provides a gentle introduction to the study of arithmetic subgroups of semisimple Lie groups. This means that the goal is to understand the group SL(n, Z) and certain of its subgroups. Among the major results discussed in the later chapters are the Mostow Rigidity Theorem, the Margulis Superrigidity Theorem, Ratner's Theorems, and the classification of arithmetic subgroups of classical groups. As background for the proofs of these theorems, the book provides primers on lattice subgroups, arithmetic groups, real rank and Q-rank, ergodic theory, unitary representations, amenability, Kazhdan's property (T), and quasi-isometries. Numerous exercises enhance the book's usefulness both as a textbook for a second-year graduate course and for self-study. In addition, notes at the end of each chapter have suggestions for further reading. (Proofs in this book often consider only an illuminating special case.) Readers are expected to have some acquaintance with Lie groups, but appendices briefly review the prerequisite background. A PDF file of the book is available on the internet. This inexpensive printed edition is for readers who prefer a hardcopy.

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Page Count

492

Published Date

ISBN 10

0986571601

ISBN 13

9780986571602

Ergodic Theory, Groups, and Geometry

NSF-CBMS Regional Research Conferences in the Mathematical Sciences, June 22-26, 1998, University of Minnesota

By: Robert J. Zimmer,Dave Witte Morris

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Ergodic Theory, Groups, and Geometry

NSF-CBMS Regional Research Conferences in the Mathematical Sciences, June 22-26, 1998, University of Minnesota

By: Robert J. Zimmer,Dave Witte Morris

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Page Count

103

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821809806

ISBN 13

9780821809808

Book's by Dave Witte Morris

Ratner's Theorems on Unipotent Flows

Ratner's Theorems on Unipotent Flows

Ratner's Theorems on Unipotent Flows

Ratner's Theorems on Unipotent Flows

Ergodic Theory, Groups, and Geometry

Ergodic Theory, Groups, and Geometry

Introduction to Arithmetic Groups

Introduction to Arithmetic Groups

Ergodic Theory, Groups, and Geometry

Ergodic Theory, Groups, and Geometry

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