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

Lingmin Liao (1) , Michal Rams (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 PAN - Institut of Mathematics - Polish Academy of Sciences

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 $k, 2k$.

Mots clés: multifractal analysis; multiple Birkhoff average; Hausdorff dimension

Domaines: Systèmes dynamiques [math.DS]

Lingmin Liao, Michal Rams. Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents. Real Analysis Exchange, 2013, 39 (1), pp.1-14. ⟨hal-00705104v2⟩