Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

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

Tom 104 / 2006

Colloquium Mathematicum 104 (2006), 193-206 MSC: 28A78, 28A80, 60J60. DOI: 10.4064/cm104-2-3

Streszczenie

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.

Autorzy

• Athanasios BatakisMAPMO
Université d'Orléans
BP 6759
45067 Orléans Cedex 2, France
e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek