TY - JOUR
T1 - Amount of failure of upper-semicontinuity of entropy in non-compact rank-one situations, and Hausdorff dimension
AU - Kadyrov, S.
AU - Pohl, A.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - 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 flows on homogeneous spaces, where is any connected semisimple Lie group of real rank one with finite center, and is any non-uniform lattice in. We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points that diverge on average.
AB - 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 flows on homogeneous spaces, where is any connected semisimple Lie group of real rank one with finite center, and is any non-uniform lattice in. We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points that diverge on average.
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U2 - 10.1017/etds.2015.55
DO - 10.1017/etds.2015.55
M3 - Article
AN - SCOPUS:84943760854
VL - 37
SP - 539
EP - 563
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
SN - 0143-3857
IS - 2
ER -