On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method

Manfred Einsiedler; Elon Lindenstrauss

doi:10.3934/jmd.2008.2.83

Article Contents

2008, Volume 2, Issue 1: 83-128. Doi: 10.3934/jmd.2008.2.83 open access

This issue Previous Article Stable ergodicity for partially hyperbolic attractors with negative central exponents Next Article Simultaneous diophantine approximation with quadratic and linear forms

On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method

Manfred Einsiedler^1, and
Elon Lindenstrauss^2,

1.
Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus OH 43210-1174
2.
Fine Hall, Washington Road, Princeton NJ 08544-1000

Received: July 31, 2007

Revised: September 30, 2007

Published: September 2007

Abstract Related Papers Cited by

Abstract

We consider measures on locally homogeneous spaces $\Gamma \backslash G$ which are invariant and have positive entropy with respect to the action of a single diagonalizable element $a \in G$ by translations, and prove a rigidity statement regarding a certain type of measurable factors of this action.
This rigidity theorem, which is a generalized and more conceptual form of the low entropy method of [14,3] is used to classify positive entropy measures invariant under a one parameter group with an additional recurrence condition for $G=G_1 \times G_2$ with $G_1$ a rank one algebraic group. Further applications of this rigidity statement will appear in forthcoming papers.

Keywords:

Mathematics Subject Classification: Primary: 37D40; Secondary: 37A35, 37A45.

Citation:

Article Metrics

HTML views() PDF downloads(195) Cited by(0)

On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content