Geodesic
Hausdorff Dimension of the Set of Generic Points for Gibbs Measures
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 68-71.

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For a Gibbs measure on the configuration space of a finite spin lattice system, we find (in terms of entropy) the Hausdorff dimension of the set of generic points. Using this result, we evaluate the Hausdorff dimension of level sets for Birkhoff ergodic averages of some continuous functions on the configuration space.
Mots-clés : Hausdorff dimension
Keywords: Gibbs measures, ergodic averages, entropy. 
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B. M. Gurevich; A. A. Tempel'man. Hausdorff Dimension of the Set of Generic Points for Gibbs Measures. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 68-71. http://geodesic.mathdoc.fr/item/FAA_2002_36_3_a8/

[1] Ruelle D., Thermodynamic Formalism, Addison-Wesley, Reading, MA, 1978 | MR | Zbl

[2] Georgi Kh.-O., Gibbsovskie mery i fazovye perekhody, Mir, M., 1992 | MR

[3] Tempelman A. A., Teor. ver. i prim., 44:3 (1999), 589–616 | DOI | MR

[4] Gurevich B. M., Tempelman A. A., “Khausdorfova razmernost i termodinamicheskii formalizm”, UMN, 54:2 (1999), 171–172 | DOI | MR | Zbl

[5] Cajar H., Billingsley dimension in probability spaces, Lect. Notes in Math., 892, Springer-Verlag, Berlin, 1988 | MR

[6] Olivier E., “Analyse multifractale de fonctions continues”, C. R. Acad. Sci. Paris Série I, 326 (1998), 1171–1174 | DOI | MR | Zbl

[7] Olivier E., “Dimension de Billingsley d'ensembles satures”, C. R. Acad. Sci. Paris Série I, 328 (1999), 13–16 | DOI | MR | Zbl

[8] Takens F., Verbitski E., “Multifractal analysis of local entropies for expansive homeomorphisms with specification”, Comm. Math. Phys., 203:3 (1999), 593–612 | DOI | MR | Zbl

[9] Takens F., Verbitski E., On the variational principle for the topological entropy of certain non-compact sets, Preprint, 1999 | MR

[10] Fan Ai-Hua, Feng De-Jun, J. Statist. Phys., 99:3/4 (2000), 813–856 | DOI | MR | Zbl

[11] Tempelman A. A., “Multifractal analysis of ergodic averages: a generalization of Eggleston's theorem”, J. Dynam. Control Systems, 7:4 (2001), 535–551 | DOI | MR | Zbl