Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and hausdorff dimension
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Date
2012
Authors
Kadyrov, Shirali
Pohl, A.
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Abstract
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 semisimple Lie group of real rank 1 with nite center, and is any nonuniform lattice in G. We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points which diverge on average.
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Keywords
Research Subject Categories::MATHEMATICS, Hausdorff dimension
Citation
Kadyrov Shirali, Pohl A.; 2012; Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and hausdorff dimension