On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process

Athanasios Batakis. "On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process." Colloquium Mathematicae 104.2 (2006): 193-206. <http://eudml.org/doc/283711>.

@article{AthanasiosBatakis2006,
abstract = {We study the Hausdorff dimension of measures whose weight distribution satisfies a Markov non-homogeneous property. We prove, in particular, that the Hausdorff dimensions of this kind of measures coincide with their lower Rényi dimensions (entropy). Moreover, we show that the packing dimensions equal the upper Rényi dimensions. As an application we get a continuity property of the Hausdorff dimension of the measures, when viewed as a function of the distributed weights under the $ℓ^\{∞\}$ norm.},
author = {Athanasios Batakis},
journal = {Colloquium Mathematicae},
keywords = {Hausdorff and packing dimensions; entropy; non-homogeneous Markov processes},
language = {eng},
number = {2},
pages = {193-206},
title = {On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process},
url = {http://eudml.org/doc/283711},
volume = {104},
year = {2006},
}

TY - JOUR
AU - Athanasios Batakis
TI - On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process
JO - Colloquium Mathematicae
PY - 2006
VL - 104
IS - 2
SP - 193
EP - 206
AB - We study the Hausdorff dimension of measures whose weight distribution satisfies a Markov non-homogeneous property. We prove, in particular, that the Hausdorff dimensions of this kind of measures coincide with their lower Rényi dimensions (entropy). Moreover, we show that the packing dimensions equal the upper Rényi dimensions. As an application we get a continuity property of the Hausdorff dimension of the measures, when viewed as a function of the distributed weights under the $ℓ^{∞}$ norm.
LA - eng
KW - Hausdorff and packing dimensions; entropy; non-homogeneous Markov processes
UR - http://eudml.org/doc/283711
ER -