Ergodic theory and topological dynamics of group actions on homogeneous spaces

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Ergodic theory and topological dynamics of group actions on homogeneous spaces / M. Bachir Bekka, Matthias Mayer

資料種別:

図書

出版情報:

Cambridge : Cambridge University Press, 2000

形態:

x, 200 p. ; 23 cm

シリーズ名:

London Mathematical Society lecture note series ; 269 <BA0005393X>

著者名:

ISBN:

9780521660303 [0521660300]

書誌ID:

BA46341433

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references (p. [189]-197) and index

主題:

Ergodic theory

言語:

英語

目次情報:

Preface

Ergodic Systems / I.：

Examples and Basic Results / 1：

Ergodic Theory and Unitary Representations / 2：

Invariant Measures and Unique Ergodicity / 3：

The Geodesic Flow of Riemannian Locally Symmetric Spaces / II.：

Some Hyperbolic Geometry

Lattices and Fundamental Domains

The Geodesic Flow of Compact Riemann Surfaces

The Geodesic Flow on Riemannian Locally Symmetric Spaces / 4：

The Vanishing Theorem of Howe and Moore / III.：

Howe--Moore's Theorem

Moore's Ergodicity Theorems

Counting Lattice Points in the Hyperbolic Plane

Mixing of All Orders

The Horocycle Flow / IV.：

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 / V.：

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 / 5：

An Application to Number Theory: Oppenheim's Conjecture / VI.：

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 / 6：

Bibliography

Index

Preface

Ergodic Systems / I.：

Examples and Basic Results / 1：

Ergodic Theory and Unitary Representations / 2：

Invariant Measures and Unique Ergodicity / 3：

The Geodesic Flow of Riemannian Locally Symmetric Spaces / II.：

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