Dimension spectrum for a nonconventional ergodic average

Details Dimension spectrum for a nonconventional ergodic average Dimension spectrum for a nonconventional ergodic average

2011-07-08

arxiv.org/abs/1107.1749v2

Mathematics

Dynamical Systems

11 pages, 1 figure; revision after the referee report (some proofs are shorter), to appear in Real Analysis Exchange

Scientific paper

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
$\theta\in [0,1]$.

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