Gurevich, B. M.; Tempelman, A. A. Multifractal analysis of time averages for continuous vector functions on configuration space. (English) Zbl 1144.28004 Theory Probab. Appl. 51, No. 1, 78-91 (2007); translation from Teor. Veroyatn. Primen. 51, No. 1, 78-94 (2006). Authors’ abstract: We consider a natural action \(\tau\) of the group \(\mathbb{Z}^d\) on the space \(X\) consisting of the functions \(x: \mathbb{Z}^d\to S\) (\(S\)-valued configuration on \(\mathbb{Z}^d\)), where \(S\) is a finite set. For an arbitrary continuous function \(f: X\to \mathbb{R}^m\), we study the multifractal spectrum of its time means corresponding to the dynamical system \(\tau\) and a proper “average” sequence of finite subsets of the lattice \(\mathbb{Z}^d\). The main tool of the research is thermodynamic formalism. Reviewer: Ning Zhong (Cincinnati) Cited in 2 Documents MSC: 28A80 Fractals 28A78 Hausdorff and packing measures Keywords:Hausdorff dimension; cylinder dimension; invariant measure; Gibbs random field; space mean; time mean; multifractal spectrum PDFBibTeX XMLCite \textit{B. M. Gurevich} and \textit{A. A. Tempelman}, Theory Probab. Appl. 51, No. 1, 78--91 (2007; Zbl 1144.28004); translation from Teor. Veroyatn. Primen. 51, No. 1, 78--94 (2006) Full Text: DOI