Ergodic theory and topological dynamics of group actions on homogeneous spacesM. Bachir Bekka, Matthias Mayer.
Bekka, M. Bachir.
Ergodic theory and topological dynamics of group actions on homogeneous spacesM. Bachir Bekka, Matthias Mayer. - Cambridge, U.K. ; New York : Cambridge University Press, (c)2000. - 1 online resource (x, 200 pages) : illustrations. - London Mathematical Society lecture note series ; 269 .
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.
9781107089273
Ergodic theory.
Topological dynamics.
Electronic Books.
QA611 / .E746 2000
Ergodic theory and topological dynamics of group actions on homogeneous spacesM. Bachir Bekka, Matthias Mayer. - Cambridge, U.K. ; New York : Cambridge University Press, (c)2000. - 1 online resource (x, 200 pages) : illustrations. - London Mathematical Society lecture note series ; 269 .
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.
9781107089273
Ergodic theory.
Topological dynamics.
Electronic Books.
QA611 / .E746 2000