Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents

Lingmin Liao, Michal Rams

Published 2012-06-07, updated 2012-06-21Version 2

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 $k, 2k$.