Abstract
Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces, where is any connected semisimple Lie group of real rank one with finite center, and is any non-uniform lattice in. We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points that diverge on average.
| Original language | English |
|---|---|
| Pages (from-to) | 539-563 |
| Number of pages | 25 |
| Journal | Ergodic Theory and Dynamical Systems |
| Volume | 37 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Apr 1 2017 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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Kadyrov, S., & Pohl, A. (2017). Amount of failure of upper-semicontinuity of entropy in non-compact rank-one situations, and Hausdorff dimension. Ergodic Theory and Dynamical Systems, 37(2), 539-563. https://doi.org/10.1017/etds.2015.55