Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents
Abstract
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding 0,1N of the attractor, we compute the Hausdorff dimension of the set of points with a given frequency of the pattern 11 in positions k, 2k.
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