Kooperativer Bibliotheksverbund

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Umfang: 1 Online-Ressource (x, 200 pages) , digital, PDF file(s).

ISBN: 9780511758898

Serie: London Mathematical Society lecture note series 269

Inhalt: 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 conjecture. Also included here: an exposition of Ratner's work on Raghunathan's conjectures; a complete proof of the Howe-Moore vanishing theorem for general semisimple Lie groups; a new treatment of Mautner's result on the geodesic flow of a Riemannian symmetric space; Mozes' result about mixing of all orders and the asymptotic distribution of lattice points in the hyperbolic plane; Ledrappier's example of a mixing action which is not a mixing of all orders. The treatment is as self-contained and elementary as possible. It should appeal to graduate students and researchers interested in dynamical systems, harmonic analysis, differential geometry, Lie theory and number theory.

Anmerkung: Title from publisher's bibliographic system (viewed on 05 Oct 2015) , 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.

Weitere Ausg.: ISBN 9780521660303

Weitere Ausg.: ISBN 9780521660303

Weitere Ausg.: ISBN 9780521660303

Weitere Ausg.: Erscheint auch als Bekka, Mohammed El Bachir Ergodic theory and topological dynamics of group actions on homogeneous spaces Cambridge [u.a.] : Cambridge Univ. Press, 2000 ISBN 0521660300

Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 9780521660303

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): Ergodentheorie ; Topologische Dynamik

DOI: 10.1017/CBO9780511758898

URL: Volltext

URL: Inhaltstext

UID:

Umfang: X, 200 S. : graph. Darst.

Ausgabe: 1. publ.

ISBN: 0-521-66030-0

Serie: London Mathematical Society: London Mathematical Society lecture note series 269

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): Ergodentheorie ; Topologische Dynamik

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009096593&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

UID:

Umfang: 1 online resource (x, 200 pages) : , digital, PDF file(s).

ISBN: 9780511758898 (ebook)

Serie: London Mathematical Society lecture note series ; 269

Inhalt: 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 conjecture. Also included here: an exposition of Ratner's work on Raghunathan's conjectures; a complete proof of the Howe-Moore vanishing theorem for general semisimple Lie groups; a new treatment of Mautner's result on the geodesic flow of a Riemannian symmetric space; Mozes' result about mixing of all orders and the asymptotic distribution of lattice points in the hyperbolic plane; Ledrappier's example of a mixing action which is not a mixing of all orders. The treatment is as self-contained and elementary as possible. It should appeal to graduate students and researchers interested in dynamical systems, harmonic analysis, differential geometry, Lie theory and number theory.

Anmerkung: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , 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.

Weitere Ausg.: Print version: ISBN 9780521660303

Sprache: Englisch

URL: https://doi.org/10.1017/CBO9780511758898

UID:

Umfang: X, 200 S. , graph. Darst. , 23 cm

Ausgabe: 1. publ.

ISBN: 0521660300

Serie: London Mathematical Society lecture note series 269

Anmerkung: Literaturverz. S. [189] - 197

Weitere Ausg.: Erscheint auch als Online-Ausgabe Bekka, M Ergodic theory and topological dynamics of group actions on homogeneous spaces Cambridge : Cambridge University Press, 2000 ISBN 9780511758898

Weitere Ausg.: Online-Ausg. (MyiLibrary) Bekka, Mohammed El Bachir Ergodic theory and topological dynamics of group actions on homogeneous spaces Cambridge : Cambridge University Press, 2000 ISBN 9781107092259

Weitere Ausg.: ISBN 9781299748941

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): Ergodentheorie ; Topologische Dynamik

URL: Inhaltsverzeichnis

URL: Inhaltstext

Mehr zum Autor: Mayer, Matthias 1969-

UID:

Umfang: 1 online resource (x, 200 pages) : , digital, PDF file(s).

ISBN: 1-139-88556-1 , 1-107-08927-1 , 1-107-10110-7 , 1-107-09225-6 , 1-107-09550-6 , 1-107-10359-2 , 0-511-75889-8

Serie: London Mathematical Society lecture note series ;

Inhalt: 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 conjecture. Also included here: an exposition of Ratner's work on Raghunathan's conjectures; a complete proof of the Howe-Moore vanishing theorem for general semisimple Lie groups; a new treatment of Mautner's result on the geodesic flow of a Riemannian symmetric space; Mozes' result about mixing of all orders and the asymptotic distribution of lattice points in the hyperbolic plane; Ledrappier's example of a mixing action which is not a mixing of all orders. The treatment is as self-contained and elementary as possible. It should appeal to graduate students and researchers interested in dynamical systems, harmonic analysis, differential geometry, Lie theory and number theory.

Anmerkung: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , 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. , English

Weitere Ausg.: ISBN 1-299-74894-5

Weitere Ausg.: ISBN 0-521-66030-0

Sprache: Englisch