Big Birkhoff sums in $d$-decaying Gauss like iterated function systems
Number Theory
2021-08-20 v3 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.1905.02547,
title = {Big Birkhoff sums in $d$-decaying Gauss like iterated function systems},
author = {Michal Rams and Lingmin Liao and Michal Rams},
journal= {arXiv preprint arXiv:1905.02547},
year = {2021}
}