Engel连分数中一个例外集的Hausdorff维数

HAUSDORFF DIMENSION OF AN EXCEPTIONAL SET IN ENCEL CONTINUED FRACTION EXPANSION

本文研究了Engel连分数展式中部分商以某种速度增长的集合的Hausdorff维数.利用自然覆盖和质量分布原理,得到了集合B(α)={x∈(0,1):■ log b_(n+1)(x)/log b_n(x)=α}的Hausdorff维数是1/α的结果.

In this article,we study the Hausdorff dimension of an exceptional set determined by partial quotients in its Engel continued fraction expansion.By using natural covering system and principle of mass distribution,we get the result that the Hausdorff dimension of the set B（α） = {x∈（0,1）：■ log b_（n＋1）（x）/log b_n（x） =α} is 1/α.