Dynamical Systems and Semisimple Groups: An Introduction

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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.
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Editorial Reviews

From the Publisher
"Well written and...highly recommended." Bulletin of the American Mathematical Society

"...excellent and quite comprehensive introduction to the algebra and dynamics of Lie group actions in the chapters..." Monatshefte fur Mathematik

"An important feature of the text is the inclusion of many exercises, always a helpful thing." Proceedings of the Edinburgh Mathematical Society

"...nicely written and highly recommended, especially for graduate students specializing in Lie groups and ergodic theory." Mathematical Reviews

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Product Details

  • ISBN-13: 9780521142168
  • Publisher: Cambridge University Press
  • Publication date: 4/1/2010
  • 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 1
2 Ergodic Theory - Part I 17
3 Smooth Actions and Lie Theory 32
4 Algebraic Actions 59
5 The Classical Groups 77
6 Geometric Structures 88
7 Semisimple Lie Groups 119
8 Ergodic Theory - Part II 149
9 Oseledec's Theorem 174
10 Rigidity Theorems 196
App. A Lattices in SL(n, R) 231
References 241
Index 243
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