Geodesic
On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process
Athanasios Batakis1
1 MAPMO Université d'Orléans BP 6759 45067 Orléans Cedex 2, France
Colloquium Mathematicum, Tome 104 (2006) no. 2, pp. 193-206

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\ell^{\infty}$ norm.
DOI : 10.4064/cm104-2-3
Keywords: study hausdorff dimension measures whose weight distribution satisfies markov non homogeneous property prove particular hausdorff dimensions kind measures coincide their lower nyi dimensions entropy moreover packing dimensions equal upper nyi dimensions application get continuity property hausdorff dimension measures viewed function distributed weights under ell infty norm

Athanasios Batakis 1

1 MAPMO Université d'Orléans BP 6759 45067 Orléans Cedex 2, France 
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Athanasios Batakis. On entropy and Hausdorff dimension of
 measures defined through a
 non-homogeneous Markov process. Colloquium Mathematicum, Tome 104 (2006) no. 2, pp. 193-206. doi: 10.4064/cm104-2-3

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