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Dynamical systems and semisimple groups : an introduction / Renato Feres

Auteur principal : Feres, Renato, 1962-, AuteurType de document : MonographieCollection : Cambridge tracts in mathematics, 126Langue : anglais.Pays : Etats Unis.Éditeur : New York : Cambridge University Press, 1998Description : 1 vol. (XVI-245 p.) ; 24 cmISBN : 0521591627.ISSN : 0950-6284.Bibliographie : Bibliogr. p. 241-242. Index.Sujet MSC : 37C85, Smooth dynamical systems: general theory, Dynamics induced by group actions other than ℤ and ℝ, and ℂ
22E40, Lie groups, Discrete subgroups of Lie groups
22F10, Noncompact transformation groups, Measurable group actions
37A15, Ergodic theory, General groups of measure-preserving transformations and dynamical systems
53C24, Global differential geometry, Rigidity results
En-ligne : Zentralblatt | MathSciNet
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The book concentrates on the dynamics of semisimple group actions on manifolds. As the author notes, "the main purpose of this book is to serve as a relatively gentle introduction to the rigidity theorems of Margulis and Zimmer''. For this reason, the exposition starts with very basic preliminaries about ergodic theory and Lie groups, and culminates with rigidity theorems for actions of a higher rank semisimple Lie group on a manifold.
The book began as a series of lectures by the author, and is a nice textbook for a student who already knows what manifold and measure are and is looking for an introduction to current trends in the theory of Lie group actions. The exposition is very well structured and, as a rule, self-contained. Numerous exercises illustrate the subject under discussion and are often essential for the following results. This makes reading more active and efficient. One of the advantages of the book is that the author does not intend to provide the results in their full generality, concentrating instead on the essential ideas. ... (MathSciNet)

Bibliogr. p. 241-242. Index

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

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