Includes bibliographies 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.

COPYRIGHT NOT covered - Click this link to request copyright permission:

https://lib.ciu.edu/copyright-request-form