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

Lingmin Liao; Michal Rams

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

Dynamical Systems 2012-06-22 v2

Authors: Lingmin Liao , Michal Rams

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 $k, 2k$ .

Keywords

multifractal analysis multiple ergodic averages iterated function system Hausdorff dimension pattern frequency Lyapunov exponents

Cite

@article{arxiv.1206.1397,
  title  = {Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents},
  author = {Lingmin Liao and Michal Rams},
  journal= {arXiv preprint arXiv:1206.1397},
  year   = {2012}
}

Comments

13 pages

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