THE RELATIVE CONVERGENCE SPEED FOR ENGEL EXPANSIONS AND HAUSDORFF DIMENSION

Zhenliang Zhang () and Xiaoyan Tan
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Zhenliang Zhang: School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China
Xiaoyan Tan: School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 04, 1-7

Abstract: In this paper, we investigate how many real numbers can be well approximated by their convergents in the Engel expansions. Furthermore, the relative growth rate of convergence speed of convergents in the Engel expansion of an irrational number is studied to the rate of growth of its digits. The Hausdorff dimension of exceptional sets of points with a given relative growth rate is established.

Keywords: Engel Expansion; Hausdorff Dimension; Relative Growth Rate (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501061

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