Exceptional sets in homogeneous spaces and Hausdorff dimension

Shirali Kadyrov

    Research output: Contribution to journal › Article

    Abstract

    In this paper, we study the dimension of a family of sets arising in open dynamics. We use exponential mixing results for diagonalizable flows in compact homogeneous spaces X to show that the Hausdorff dimension of set of points that lie on trajectories missing a particular open ball of radius r is at most where C > 0 is a constant independent of r > 0. Meanwhile, we also describe a general method for computing the least cardinality of open covers of dynamical sets using volume estimates.

    Original languageEnglish
    Pages (from-to)149-157
    Number of pages9
    JournalDynamical Systems
    Volume30
    Issue number2
    DOIs
    Publication statusPublished - Apr 3 2015

    Fingerprint

    Exceptional Sets
    Homogeneous Space
    Hausdorff Dimension
    Trajectories
    Open cover
    Compact Space
    Set of points
    Cardinality
    Ball
    Radius
    Trajectory
    Computing
    Estimate
    Family

    Keywords

    • exponential mixing
    • Hausdorff dimension
    • homogeneous dynamics
    • open dynamics

    ASJC Scopus subject areas

    • Mathematics(all)
    • Computer Science Applications

    Cite this

    Exceptional sets in homogeneous spaces and Hausdorff dimension. / Kadyrov, Shirali.

    In: Dynamical Systems, Vol. 30, No. 2, 03.04.2015, p. 149-157.

    Research output: Contribution to journal › Article

    Kadyrov, S 2015, 'Exceptional sets in homogeneous spaces and Hausdorff dimension', Dynamical Systems, vol. 30, no. 2, pp. 149-157. https://doi.org/10.1080/14689367.2014.990871
    Kadyrov S. Exceptional sets in homogeneous spaces and Hausdorff dimension. Dynamical Systems. 2015 Apr 3;30(2):149-157. https://doi.org/10.1080/14689367.2014.990871
    Kadyrov, Shirali. / Exceptional sets in homogeneous spaces and Hausdorff dimension. In: Dynamical Systems. 2015 ; Vol. 30, No. 2. pp. 149-157.
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