Geodesic
Gibbs measures in a markovian context and dimension
L. Farhane1 ; G. Michon2
1Faculté des sciences de Monastir 5000 Monastir, Tunisie
2Laboratoire de topologie UMR 5584 Université de Bourgogne B.P. 400 21011 Dijon, France
Colloquium Mathematicum, Tome 88 (2001) no. 2, pp. 215-223

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DOI

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 $[0, 1\mathclose [$ and $[0, 1\mathclose [^2$. 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.
DOI : 10.4064/cm88-2-4
Keywords: main gibbs measures markovian matrices context general context compute hausdorff dimension subsets mathclose mathclose introduce parameter which could interpreted within thermodynamic framework variable conjugate energy particular cases recover shannon mcmillan breiman eggleston theorems proofs deeply rooted properties non negative irreducible matrices large deviations techniques introduced ellis

L. Farhane  1   ; G. Michon  2

1 Faculté des sciences de Monastir 5000 Monastir, Tunisie
2 Laboratoire de topologie UMR 5584 Université de Bourgogne B.P. 400 21011 Dijon, France 
L. Farhane; G. Michon. Gibbs measures in a markovian context and dimension. Colloquium Mathematicum, Tome 88 (2001) no. 2, pp. 215-223. doi: 10.4064/cm88-2-4
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