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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.

MSC:

28A80 Fractals
28A78 Hausdorff and packing measures
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