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 \(\{0,1\}^{\mathbb{N}}\) of the attractor, we compute the Hausdorff dimension of the set of points with a given frequency of the pattern \(11\) in positions \(k, 2k\).