Ergodic theory and topological dynamics of group actions on homogeneous spaces /

The study of geodesic flows on homogenous spaces is an area of research that has yielded some fascinating developments. This book, first published in 2000, focuses on many of these, and one of its highlights is an elementary and complete proof (due to Margulis and Dani) of Oppenheim's conjectur...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bekka, M. Bachir
Otros Autores: Mayer, Matthias (Mathematician)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, U.K. ; New York : Cambridge University Press, 2000.
Colección:London Mathematical Society lecture note series ; 269.
Temas:
Ergodic theory.
Topological dynamics.
Théorie ergodique.
Dynamique topologique.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Ergodiciteit.
Topologische groepen.
Dynamische systemen.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Ergodic Systems
  • Examples and Basic Results
  • Ergodic Theory and Unitary Representations
  • Invariant Measures and Unique Ergodicity
  • The Geodesic Flow of Riemannian Locally Symmetric Spaces
  • Some Hyperbolic Geometry
  • Lattices and Fundamental Domains
  • The Geodesic Flow of Compact Riemann Surfaces
  • The Geodesic Flow on Riemannian Locally Symmetric Spaces
  • The Vanishing Theorem of Howe and Moore
  • Howe--Moore's Theorem
  • Moore's Ergodicity Theorems
  • Counting Lattice Points in the Hyperbolic Plane
  • Mixing of All Orders
  • The Horocycle Flow
  • The Horocycle Flow of a Riemann Surface
  • Proof of Hedlund's Theorem--Cocompact Case
  • Classification of Invariant Measures
  • Equidistribution of Horocycle Orbits
  • Siegel Sets, Mahler's Criterion and Margulis' Lemma
  • Siegel Sets in SL(n, R)
  • SL(n, Z) is a lattice in SL(n, R)
  • Mahler's Criterion
  • Reduction of Positive Definite Quadratic Forms
  • Margulis' Lemma
  • An Application to Number Theory: Oppenheim's Conjecture
  • Oppenheim's Conjecture
  • Proof of the Theorem--Preliminaries
  • Existence of Minimal Closed Subsets
  • Orbits of One-Parameter Groups of Unipotent Linear Transformations
  • Proof of the Theorem--Conclusion
  • Ratner's Results on the Conjectures of Raghunathan, Dani and Margulis.

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