Real Analysis Exchange

Dimension Spectrum for a Nonconventional Ergodic Average

Yuval Peres and Boris Solomyak

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Abstract

We compute the dimension spectrum of certain nonconventional averages, namely, the Hausdorff dimension of the set of \(0,1\) sequences, for which the frequency of the pattern 11 in positions \(k, 2k\) equals a given number \(\theta\in [0,1]\).

Article information

Source
Real Anal. Exchange, Volume 37, Number 2 (2011), 375-388.

Dates
First available in Project Euclid: 15 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.rae/1366030632

Mathematical Reviews number (MathSciNet)
MR3080599

Zentralblatt MATH identifier
1287.37015

Subjects
Primary: 28A80: Fractals [See also 37Fxx] 37C45: Dimension theory of dynamical systems
Secondary: 28A78: Hausdorff and packing measures

Keywords
multifractal analysis multiple Birkhoff average Hausdorff dimension

Citation

Peres, Yuval; Solomyak, Boris. Dimension Spectrum for a Nonconventional Ergodic Average. Real Anal. Exchange 37 (2011), no. 2, 375--388. https://projecteuclid.org/euclid.rae/1366030632


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