Dynamical Systems and Semisimple Groups: An Introduction

Dynamical Systems and Semisimple Groups: An Introduction

by Renato Feres
     
 

This book comprises a systematic, self-contained introduction to the Margulis-Zimmer theory and provides an entry into current research. Taking as prerequisites only the standard first-year graduate courses in mathematics, the author develops in a detailed and self-contained way the main results on Lie groups, Lie algebras, and semisimple groups, including basic facts… See more details below

Overview

This book comprises a systematic, self-contained introduction to the Margulis-Zimmer theory and provides an entry into current research. Taking as prerequisites only the standard first-year graduate courses in mathematics, the author develops in a detailed and self-contained way the main results on Lie groups, Lie algebras, and semisimple groups, including basic facts normally covered in first courses on manifolds and Lie groups plus topics such as integration of infinitesimal actions of Lie groups. He then derives the basic structure theorems for the real semisimple Lie groups, such as the Cartan and Iwasawa decompositions, and gives an extensive exposition of the general facts and concepts from topological dynamics and ergodic theory, including detailed proofs of the multiplicative ergodic theorem and Moore's ergodicity theorem.

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
1Topological Dynamics1
2Ergodic Theory - Part I17
3Smooth Actions and Lie Theory32
4Algebraic Actions59
5The Classical Groups77
6Geometric Structures88
7Semisimple Lie Groups119
8Ergodic Theory - Part II149
9Oseledec's Theorem174
10Rigidity Theorems196
App. ALattices in SL(n, R)231
References241
Index243

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