Geodesic
Multifractal analysis of time averages for continuous vector functions on configuration space
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 78-94

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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.
Mots-clés : Hausdorff dimension
Keywords: cylinder dimension, invariant measure, Gibbs random field, space mean, time mean, multifractal spectrum. 
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     title = {Multifractal analysis of time averages for continuous vector functions on configuration space},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {78--94},
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     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_1_a5/}
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B. M. Gurevich; A. A. Tempel'man. Multifractal analysis of time averages for continuous vector functions on configuration space. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 78-94. http://geodesic.mathdoc.fr/item/TVP_2006_51_1_a5/