Dynamical Systems and Semisimple Groups: An Introduction (Cambridge Tracts in Mathematics, Series Number 126) - Hardcover

Feres, Renato

Hardcover

ISBN 10: 0521591627 ISBN 13: 9780521591621

Publisher: Cambridge University Press, 1998

Synopsis

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.

About this title

Book Description

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.

Review

"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

Edition details

• Publisher: Cambridge University Press
• Publication date: 1998
• Language: English
• ISBN 10: 0521591627
• ISBN 13: 9780521591621
• Binding: Hardcover
• Edition number: 1
• Number of pages: 264