Define the recurrence set of Gauss transformation $T$ on the field of Laurent series as following
$$E(x_0)=\{x\in I: T^n(x)\in I_{t_n}(x_0) for infinitely many $n$\},$$ where $I_{t_n}(x_0)$ denotes $t_n$-th order cylinder of $x_0$. In this paper, the Hausdorff dimension of the set $E(x_0)$ is determined.
Publié le : 2010-12-15
Classification:
continued fraction,
recurrence set,
formal Laurent series,
Hausdorff dimension,
11K55,
28A80,
58F03
@article{1291903395,
author = {Zhang, Lan and Wang, Sikui},
title = {Hausdorff dimension of the recurrence sets of Gauss transformation on the field of Laurent series},
journal = {Funct. Approx. Comment. Math.},
volume = {42},
number = {1},
year = {2010},
pages = { 161-170},
language = {en},
url = {http://dml.mathdoc.fr/item/1291903395}
}
Zhang, Lan; Wang, Sikui. Hausdorff dimension of the recurrence sets of Gauss transformation on the field of Laurent series. Funct. Approx. Comment. Math., Tome 42 (2010) no. 1, pp. 161-170. http://gdmltest.u-ga.fr/item/1291903395/