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 | |
| 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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Cite this
Kadyrov, S. (2015). Exceptional sets in homogeneous spaces and Hausdorff dimension. Dynamical Systems, 30(2), 149-157. https://doi.org/10.1080/14689367.2014.990871