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

B. M. Gurevich   ; A. A. Tempel'man

Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 78-94

Résumé

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.

Détail

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

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