Israel Journal of Mathematics

, Volume 210, Issue 1, pp 245–295 | Cite as

Escape of mass and entropy for diagonal flows in real rank one situations

Article

Abstract

Let G be a connected semisimple Lie group of real rank 1 with finite center, let Γ be a non-uniform lattice in G and a any diagonalizable element in G. We investigate the relation between the metric entropy of a acting on the homogeneous space Γ\G and escape of mass. Moreover, we provide bounds on the escaping mass and, as an application, we show that the Hausdorff dimension of the set of orbits (under iteration of a) which miss a fixed open set is not full.

Keywords

Symmetric Space Homogeneous Space Haar Measure Fundamental Domain Height Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 2015

Authors and Affiliations

  1. 1.Departement MathematikETH ZürichZürichSwitzerland
  2. 2.School of MathematicsUniversity of BristolBristolUK
  3. 3.Mathematisches InstitutGeorg-August-Universität GöttingenGöttingenGermany

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