Dynamical Systems and Semisimple Groups
An Introduction

An introduction to dynamical systems and ergodic theory with an emphasis on smooth actions of noncompact Lie groups.

Renato Feres (Author)

9780521591621, Cambridge University Press

Hardback, published 13 June 1998

264 pages
23.5 x 16 x 2.3 cm, 0.52 kg

Review of the hardback: 'This text might well become a standard one …'. G. Pilz, Internationale Mathematische Nachrichten

This 1998 book provides an introduction to dynamical systems and ergodic theory with an emphasis on smooth actions of noncompact Lie groups. The main goal is to serve as an entry into the literature on the ergodic theory of measure preserving actions of semisimple Lie groups. The author develops in a detailed and self-contained way the main results on Lie groups, Lie algebras, and semisimple groups, including basic facts 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. This book should appeal to anyone interested in Lie theory, differential geometry and dynamical systems.

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.

Subject Areas: Calculus & mathematical analysis [PBK]