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摘要
This paper is concerned with the Diophantine properties of the orbits of real numbers in continued fraction system under the doubling metric. More precisely, let phi be a positive function defined on N. We determine the Lebesgue measure and Hausdorff dimension of the set E(phi) = {(x, y) is an element of [0, 1) x [0, 1) : vertical bar T-n x - y vertical bar < phi (n) for i.m.n}, where T is the Gauss map and "i.m." stands for " infinitely many".
- 出版日期2018-1
- 单位华中科技大学
