Exceptional sets in homogeneous spaces and Hausdorff dimension

Shirali Kadyrov

doi:10.1080/14689367.2014.990871

Exceptional sets in homogeneous spaces and Hausdorff dimension

Shirali Kadyrov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	149-157
Number of pages	9
Journal	Dynamical Systems
Volume	30
Issue number	2
DOIs	https://doi.org/10.1080/14689367.2014.990871
Publication status	Published - Apr 3 2015

Keywords

Hausdorff dimension
exponential mixing
homogeneous dynamics
open dynamics

ASJC Scopus subject areas

Mathematics(all)
Computer Science Applications

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AB - 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.

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KW - exponential mixing

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KW - open dynamics

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Exceptional sets in homogeneous spaces and Hausdorff dimension

Abstract

Keywords

ASJC Scopus subject areas

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