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

    4 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 (Formula presented.), where (Formula presented.) is any connected semisimple Lie group of real rank one with finite center, and (Formula presented.) is any non-uniform lattice in (Formula presented.). 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
    JournalErgodic Theory and Dynamical Systems
    DOIs
    Publication statusAccepted/In press - Oct 6 2015

    Fingerprint

    Lie groups
    Upper Semicontinuity
    Hausdorff Dimension
    Entropy
    Metric Entropy
    Semisimple Lie Group
    Homogeneous Space
    Diverge
    Set of points

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

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    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 (Formula presented.), where (Formula presented.) is any connected semisimple Lie group of real rank one with finite center, and (Formula presented.) is any non-uniform lattice in (Formula presented.). 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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    AB - 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 (Formula presented.), where (Formula presented.) is any connected semisimple Lie group of real rank one with finite center, and (Formula presented.) is any non-uniform lattice in (Formula presented.). 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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