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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 3, Pages 68–71
DOI: https://doi.org/10.4213/faa207 (Mi faa207) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

Hausdorff Dimension of the Set of Generic Points for Gibbs Measures

B. M. Gurevicha, A. A. Tempel'manb

a M. V. Lomonosov Moscow State University
b Pennsylvania State University
Full-text PDF (146 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa207
Abstract: 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.
Keywords: Hausdorff dimension, Gibbs measures, ergodic averages, entropy.
Received: 07.08.2001
English version:
Functional Analysis and Its Applications, 2002, Volume 36, Issue 3, Pages 225–227
DOI: https://doi.org/10.1023/A:1020106306834
Bibliographic databases:
Document Type: Article
UDC: 517.938
Language: Russian
Citation: B. M. Gurevich, A. A. Tempel'man, “Hausdorff Dimension of the Set of Generic Points for Gibbs Measures”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 68–71; Funct. Anal. Appl., 36:3 (2002), 225–227
Citation in format AMSBIB
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  • https://doi.org/10.4213/faa207
  • https://www.mathnet.ru/eng/faa/v36/i3/p68
    • This publication is cited in the following 4 articles:
    1. Kleptsyn V., Ryzhov D., Minkov S., “Special Ergodic Theorems and Dynamical Large Deviations”, Nonlinearity, 25:11 (2012), 3189–3196  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. V. A. Kleptsyn, P. S. Saltykov, “On C2-stable effects of intermingled basins of attractors in classes of boundary-preserving maps”, Trans. Moscow Math. Soc., 72 (2011), 193–217  mathnet  crossref  zmath  elib
    3. Gurevich, BM, “Markov approximation of homogeneous lattice random fields”, Probability Theory and Related Fields, 131:4 (2005), 519  crossref  mathscinet  zmath  isi  scopus
    4. Gurevich, BM, “Hausdorff dimension of sets of generic points for Gibbs measures”, Journal of Statistical Physics, 108:5–6 (2002), 1281  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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