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Preliminaries Ergodicity and mixing of homogeneous flows

Dynamics of unipotent flows

Dynamics of nonunipotent flows

Applications to number theory

References

Index

Preliminaries Ergodicity and mixing of homogeneous flows

Dynamics of unipotent flows

Dynamics of nonunipotent flows

目次情報: 続きを見る

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：

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