A canonical thickening of ℚ and the entropy of α-continued fraction transformations
A canonical thickening of ℚ and the entropy of α-continued fraction transformations
复制标题
DOI：
10.1017/s0143385711000447
复制
发表时间：
2011-09
影响因子：
0.9
通讯作者：
Carlo Carminati;G. Tiozzo
中科院分区：
文献类型：
--
作者：
Carlo Carminati;G. Tiozzo
摘要 我们构造了包含在 (0,1] 中的可数开区间族，其端点是二次余数，并且它们的并集是一个完整测度集。然后我们证明这些区间正是 α 连分数熵的单调区间，从而证明了 Nakada 和 Natsui 的猜想。
Abstract We construct a countable family of open intervals contained in (0,1] whose endpoints are quadratic surds and such that their union is a full measure set. We then show that these intervals are precisely the monotonicity intervals of the entropy of α-continued fractions, thus proving a conjecture of Nakada and Natsui.