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 |
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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