Ergodic theory and topological dynamics of group actions on homogeneous spaces - Bekka, M. Bachir (Cambridge University Press, 2000)
Includes bibliographical references (p. [189]-197) and index
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