Dynamical Systems and Semisimple Groups An Introduction
Dynamical Systems and Semisimple Groups An Introduction by Renato Feres, published by Cambridge University Press on June 13, 1998, is a comprehensive resource for those delving into the fields of dynamical systems and ergodic theory. This edition spans 245 pages and is presented in English. The book focuses on smooth actions of noncompact Lie groups, aiming to provide a solid foundation for students who have completed standard first-year graduate mathematics courses.
Readers will find a detailed and self-contained exploration of key concepts related to Lie groups, Lie algebras, and semisimple groups. The text covers essential topics typically included in introductory courses on manifolds and Lie groups, alongside advanced subjects such as the integration of infinitesimal actions. The author also presents fundamental structure theorems for real semisimple Lie groups, including the Cartan and Iwasawa decompositions. Additionally, the book offers an extensive discussion of topological dynamics and ergodic theory, featuring thorough proofs of significant theorems. This work is suitable for those interested in mathematics, particularly in areas such as algebra, calculus, and geometry.
Official synopsis Publisher
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.
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