Big Birkhoff sums in $d$-decaying Gauss like iterated function systems
Volume 264 / 2022
Studia Mathematica 264 (2022), 1-25
MSC: Primary 11K50; Secondary 37E05, 28A80.
DOI: 10.4064/sm201031-23-8
Published online: 26 November 2021
Abstract
The increasing rate of the Birkhoff sums in 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 found.
