Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-17T05:35:46.182Z Has data issue: false hasContentIssue false

Positive entropy invariant measures on the space of lattices with escape of mass

Published online by Cambridge University Press:  27 January 2011

SHIRALI KADYROV*
Affiliation:
Mathematics Department, The Ohio State University, Columbus, Ohio, USA (email: shirali.kadyrov@bristol.ac.uk)

Abstract

On the space of unimodular lattices, we construct a sequence of invariant probability measures under a singular diagonal element with high entropy, and show that the limit measure is zero.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Cheung, Y.. Hausdorff dimension of the set of singular pairs. Ann. of Math. (2) to appear.Google Scholar
[2]Einsiedler, M. and Kadyrov, S.. Escape of mass and entropy for SL 3(ℤ)∖SL 3(ℝ). Preprint, arXiv:0912.0475.Google Scholar
[3]Margulis, G. A. and Tomanov, G. M.. Invariant measures for actions of unipotent groups over local fields on homogeneous spaces. Invent. Math. 116(1–3) (1994), 347392.CrossRefGoogle Scholar
[4]Sakai, T.. Riemannian Geometry (Translations of Mathematical Monographs, 149). AMS, 1996.CrossRefGoogle Scholar
[5]Walters, P.. An Introduction to Ergodic Theory. Springer, Berlin, 2000.Google Scholar