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

• Autorzy: Athanasios Batakis
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 104
• Numer: 2
• Strony: 193-206

Daty

wydano

2006

Twórcy

autor

Athanasios Batakis

• MAPMO, Université d'Orléans, BP 6759, 45067 Orléans Cedex 2, France

Identyfikatory

DOI

10.4064/cm104-2-3