Gibbs measures in a markovian context and dimension

• Autorzy: L. Farhane , G. Michon
• Języki publikacji: EN

Abstrakty

EN

The main goal is to use Gibbs measures in a markovian matrices context and in a more general context, to compute the Hausdorff dimension of subsets of [0, 1[ and [0, 1[². We introduce a parameter t which could be interpreted within thermodynamic framework as the variable conjugate to energy. In some particular cases we recover the Shannon-McMillan-Breiman and Eggleston theorems. Our proofs are deeply rooted in the properties of non-negative irreducible matrices and large deviations techniques as introduced by Ellis.

Kategorie tematyczne

• 60F10: Large deviations
• 60J05: Discrete-time Markov processes on general state spaces
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 88
• Numer: 2
• Strony: 215-223

Daty

wydano

2001

Twórcy

autor

L. Farhane

• Faculté des sciences de Monastir, 5000 Monastir, Tunisie

autor

G. Michon

• Laboratoire de topologie UMR 5584, Université de Bourgogne, B.P. 400, 21011 Dijon, France

Identyfikatory

DOI

10.4064/cm88-2-4