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Dynamical Systems and Semisimple Groups : An Introduction - Renato Feres

Dynamical Systems and Semisimple Groups

An Introduction


Published: 1st November 2008
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Here is 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 current literature on the ergodic theory of measure preserving actions of semisimple Lie groups for students who have taken 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. This book should appeal to anyone interested in Lie theory, differential geometry and dynamical systems.

'This text might well become a standard one ...'. G. Pilz, Internationale Mathematische Nachrichten

Topological dynamics
Ergodic theory
Smooth actions and Lie theory
Algebraic actions
The classical groups
Geometric structures
Semisimple Lie groups
Ergodic theory
Oseledec's theorem
Rigidity theorems
Appendix: Lattices in SL(n, R)
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521591621
ISBN-10: 0521591627
Series: Cambridge Tracts in Mathematics (Hardcover)
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 264
Published: 1st November 2008
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.91
Weight (kg): 0.56