科研之友
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摘要
Let Q be an infinite set of positive integers. Denote by W-tau,W-n(Q) (respectively, W-tau,W-n) the set of points in dimension n >= 1 that are simultaneously tau-approximable by infinitely many rationals with denominators in Q (respectively, in N*). When n >= 2 and tau > 1 + 1/(n - 1), a non-trivial lower bound for the Hausdorff dimension of the liminf set W-tau,W-n\W-tau,W-n(Q) is established in the case where the set Q satisfies some divisibility properties. The computation of the actual value of this Hausdorff dimension and the one-dimensional analogue of the problem are also discussed.
- 出版日期2013-1
