Approximation orders of real numbers by beta-expansions
Approximation orders of real numbers by beta-expansions
复制标题
通过 beta 展开的实数近似阶
DOI：
10.1007/s00209-019-02402-w
复制
发表时间：
2020
影响因子：
0.8
通讯作者：
Li Bing
中科院分区：
文献类型：
--
作者：
Fang Lulu;Wu Min;Li Bing
我们证明了几乎所有的真实的数（关于勒贝格测度）都可以用它们的指数级展开式的收敛性来逼近.此外，还确定了所有其它阶逼近的真实的数集合的Hausdorff维数.这些结果也被应用于研究变换下的真实的数的轨道、收缩目标型问题、丢番图逼近和-展开式的游程函数。
We prove that almost all real numbers (with respect to Lebesgue measure) are approximated by the convergents of their-expansions with the exponential order. Moreover, the Hausdorff dimensions of sets of the real numbers which are approximated by all other orders, are determined. These results are also applied to investigate the orbits of real numbers under-transformation, the shrinking target type problem, the Diophantine approximation and the run-length function of-expansions.