Dynamical Systems and Semisimple Groups

An Introduction
Erscheinungsjahr 2008
ISBN: 978-0-521-59162-1
Verlag: Cambridge University Press

Buch, Englisch, Band 126, 264 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 584 g

Reihe: Cambridge Tracts in Mathematics

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.

Autoren/Hrsg.

Feres, Renato

Bollobas, Bela

Fulton, W.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

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.