Amount of failure of upper-semicontinuity of entropy in non-compact rank-one situations, and Hausdorff dimension

S. Kadyrov, A. Pohl

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish
Pages (from-to)539-563
Number of pages25
JournalErgodic Theory and Dynamical Systems
Volume37
Issue number2
DOIs
Publication statusPublished - Apr 1 2017

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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