Dynamical Systems and Semisimple Groups: An Introduction

Dynamical Systems and Semisimple Groups: An Introduction

by Renato Feres
     
 

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ISBN-10: 0521142164

ISBN-13: 9780521142168

Pub. Date: 04/01/2010

Publisher: Cambridge University Press

The theory of dynamical systems can be described as the study of the global properties of groups of transformations. The historical roots of the subject lie in celestial and statistical mechanics, for which the group is the time parameter. The more general modern theory treats the dynamical properties of the semisimple Lie groups. Some of the most fundamental

Overview

The theory of dynamical systems can be described as the study of the global properties of groups of transformations. The historical roots of the subject lie in celestial and statistical mechanics, for which the group is the time parameter. The more general modern theory treats the dynamical properties of the semisimple Lie groups. Some of the most fundamental discoveries in this area are due to the work of G.A. Margulis and R. Zimmer. This book comprises a systematic, self-contained introduction to the Margulis-Zimmer theory, and provides an entry into current research. Assuming only a basic knowledge of manifolds, algebra, and measure theory, this book should appeal to anyone interested in Lie theory, differential geometry and dynamical systems.

Product Details

ISBN-13:
9780521142168
Publisher:
Cambridge University Press
Publication date:
04/01/2010
Series:
Cambridge Tracts in Mathematics Series, #126
Pages:
264
Product dimensions:
6.00(w) x 9.00(h) x 0.90(d)

Table of Contents

Preface; 1. Topological dynamics; 2. Ergodic theory - part I; 3. Smooth actions and Lie theory; 4. Algebraic actions; 5. The classical groups; 6. Geometric structures; 7. Semisimple Lie groups; 8. Ergodic theory - part II; 9. Oseledec's theorem; 10. Rigidity theorems; Appendix: Lattices in SL(n, R); References; Index.

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