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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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

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

First available in Project Euclid: 9 December 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

continued fraction recurrence set formal Laurent series Hausdorff dimension


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.

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