Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents
Résumé
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding $\{0,1\}^{\mathbb{N}}$ 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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