Browsing by Subject "Hausdorff dimension"

Now showing items 1-4 of 4

Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and hausdorff dimension

Kadyrov, Shirali; Pohl, A. (2012)

Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal ows on homogeneous spaces 􀀀nG, where G is any connected ...
Effective uniqueness of parry measure and exceptional sets in ergodic theory

Kadyrov, Shirali (2014)

It is known that hyperbolic dynamical systems admit a unique invariant probability measure with maximal entropy. We prove an effective version of this statement and use it to estimate an upper bound for Hausdorff dimension ...
Escape of mass and entropy for diagonal flows in real rank one situations

Einsiedler, M.; Kadyrov, Shirali; Pohl, A. (2011)

Let G be a connected semisimple Lie group of real rank 1 with finite center, let 􀀀 be a non-uniform lattice in G and a any diagonalizable element in G. We investigate the relation between the metric entropy of a acting ...
Exceptional sets in homogeneous spaces and hausdorff dimension

Kadyrov, Shirali (2015)

In this paper we study the dimension of a family of sets arising in open dynamics. We use exponential mixing results for diagonalizable ows in compact homogeneous spaces X to show that the Hausdorff dimension of set of ...