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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 1, Pages 78–94 (Mi tvp147)  

This article is cited in 1 scientific paper (total in 1 paper)

Multifractal analysis of time averages for continuous vector functions on configuration space

B. M. Gurevicha, A. A. Tempel'manb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Pennsylvania State University

Abstract: We consider a natural action $\tau$ of the group $Z^d$ on the space $X$ consisting of the functions $x\colonZ^d\to S$ ($S$-valued configurations on $Z^d$), where $S$ is a finite set. For an arbitrary continuous function $f\colon X\toR^m$, we study the multifractal spectrum of its time means corresponding to the dynamical system $\tau$ and a proper “averaging” sequence of finite subsets of the lattice $Z^d$. The main tool of the research is thermodynamic formalism.

Keywords: Hausdorff dimension, cylinder dimension, invariant measure, Gibbs random field, space mean, time mean, multifractal spectrum.

DOI: https://doi.org/10.4213/tvp147

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English version:
Theory of Probability and its Applications, 2007, 51:1, 78–91

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Received: 23.11.2005

Citation: B. M. Gurevich, A. A. Tempel'man, “Multifractal analysis of time averages for continuous vector functions on configuration space”, Teor. Veroyatnost. i Primenen., 51:1 (2006), 78–94; Theory Probab. Appl., 51:1 (2007), 78–91

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gurevich B.M., Tempelman A.A., “A Breiman type theorem for Gibbs measures”, J. Dyn. Control Syst., 13:3 (2007), 363–371  crossref  mathscinet  zmath  isi  elib  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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