Big Birkhoff sums in $d$-decaying Gauss like iterated function systems

Lingmin Liao (1) , Michal Rams (2)

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

The increasing rate of the Birkhoff sums in the infinite iterated function systems with polynomial decay of the derivative (for example the Gauss map) is studied. For different unbounded potential functions, the Hausdorff dimensions of the sets of points whose Birkhoff sums share the same increasing rate are obtained.

Domaines: Théorie des nombres [math.NT]; Systèmes dynamiques [math.DS]

Lingmin Liao, Michal Rams. Big Birkhoff sums in $d$-decaying Gauss like iterated function systems. 2019. ⟨hal-02119677v1⟩