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December 2010 Hausdorff dimension of the recurrence sets of Gauss transformation on the field of Laurent series
Sikui Wang, Lan Zhang
Funct. Approx. Comment. Math. 43(2): 161-170 (December 2010). DOI: 10.7169/facm/1291903395
Abstract

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.

Copyright © 2010 Adam Mickiewicz University
Sikui Wang and Lan Zhang "Hausdorff dimension of the recurrence sets of Gauss transformation on the field of Laurent series," Functiones et Approximatio Commentarii Mathematici 43(2), 161-170, (December 2010). https://doi.org/10.7169/facm/1291903395
Published: December 2010
Vol.43 • No. 2 • December 2010
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