Exceptional sets in homogeneous spaces and Hausdorff dimension

Shirali Kadyrov

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)149-157
Number of pages9
JournalDynamical Systems
Volume30
Issue number2
DOIs
Publication statusPublished - Apr 3 2015

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications

Fingerprint Dive into the research topics of 'Exceptional sets in homogeneous spaces and Hausdorff dimension'. Together they form a unique fingerprint.

Cite this