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Look Inside Dynamical Systems and Semisimple Groups

Dynamical Systems and Semisimple Groups
An Introduction

$60.99 (C)

Part of Cambridge Tracts in Mathematics

  • Date Published: April 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521142168

$ 60.99 (C)

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About the Authors
  • 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.

    • Fills gap for beginning graduate students and mathematicians in other fields
    • Geometric and dynamical perspective should appeal to a wide readership
    • Can be used as an introduction to general Lie theory and semisimple groups, topological dynamics and ergodic theory, and algebraic geometry
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    Reviews & endorsements

    "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

    • Date Published: April 2010
    • format: Paperback
    • isbn: 9780521142168
    • length: 264 pages
    • dimensions: 229 x 152 x 15 mm
    • weight: 0.39kg
    • availability: Available
  • Table of Contents

    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)

  • Author

    Renato Feres, Washington University, St Louis

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