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

  • S. KADYROV (a1) and A. POHL (a2)
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 $\unicode[STIX]{x1D6E4}\setminus G$ , where $G$ is any connected semisimple Lie group of real rank one with finite center, and $\unicode[STIX]{x1D6E4}$ is any non-uniform lattice in $G$ . 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.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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