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

TL;DR

This paper investigates the Hausdorff dimension of specific pattern frequencies in points generated by iterated function systems with non-constant Lyapunov exponents, using multifractal analysis and dynamical coding.

Contribution

It introduces a multifractal analysis approach to compute the Hausdorff dimension of pattern frequency sets in systems with non-constant Lyapunov exponents.

Findings

Computed Hausdorff dimension for pattern frequency sets

Applied multifractal analysis to systems with non-constant Lyapunov exponents

Used dynamical coding to analyze iterated function systems

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 $k, 2k$.