Kadyrov Sh.2025-08-122025-08-122015Kadyrov Sh / Exceptional sets in homogeneous spaces and Hausdorff dimension / Dynamical Systems An International Journal / 20151468-9367https://repository.sdu.edu.kz/handle/123456789/1867In 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 dim X + C rdim X log r , 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.enexponential mixinghomogeneous dynamicsHausdorff dimensionArticle