Functiones et Approximatio Commentarii Mathematici

Hausdorff dimension of the recurrence sets of Gauss transformation on the field of Laurent series

Sikui Wang and Lan Zhang

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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.

Article information

Source
Funct. Approx. Comment. Math., Volume 43, Number 2 (2010), 161-170.

Dates
First available in Project Euclid: 9 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.facm/1291903395

Digital Object Identifier
doi:10.7169/facm/1291903395

Mathematical Reviews number (MathSciNet)
MR2767168

Zentralblatt MATH identifier
1222.11099

Subjects
Primary: 11K55: Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]
Secondary: 28A80: Fractals [See also 37Fxx] 58F03

Keywords
continued fraction recurrence set formal Laurent series Hausdorff dimension

Citation

Zhang, Lan; Wang, Sikui. Hausdorff dimension of the recurrence sets of Gauss transformation on the field of Laurent series. Funct. Approx. Comment. Math. 43 (2010), no. 2, 161--170. doi:10.7169/facm/1291903395. https://projecteuclid.org/euclid.facm/1291903395


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