Badly approximable numbers and vectors in Cantor-like sets
Badly approximable numbers and vectors in Cantor-like sets
复制标题
类康托尔集中的差近似数和向量
DOI：
10.1090/s0002-9939-2011-11105-5
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发表时间：
2012
期刊：
影响因子：
10.2
通讯作者：
Hemangi Shah
中科院分区：
文献类型：
--
作者：
S. Dani;Hemangi Shah
我们证明了当d >= 2时，一类R-d，d >= 1的Cantor-like集包含了不可数多的差逼近数和差逼近向量.对于在研究对应于具有常负曲率和有限体积的（d+1）维流形的测地线流时产生的R-d的子集，也证明了一个类似的结果，推广了R中的坏逼近数集。此外，我们描述了一个条件集，这是由一个大的类，确保这些康托集的大交集。
We show that a large class of Cantor-like sets of R-d, d >= 1, contains uncountably many badly approximable numbers, respectively badly approximable vectors, when d >= 2. An analogous result is also proved for subsets of R-d arising in the study of geodesic flows corresponding to (d+1)-dimensional manifolds of constant negative curvature and finite volume, generalizing the set of badly approximable numbers in R. Furthermore, we describe a condition on sets, which is fulfilled by a large class, ensuring a large intersection with these Cantor-like sets.