BADLY APPROXIMABLE NUMBERS AND VECTORS IN CANTOR-LIKE SETS

被引：7

作者：

Dani, S. G. ^{[1
]}

Shah, Hemangi ^{[2
]}

机构：

[1] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India

[2] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 140卷 / 08期

关键词：

SCHMIDTS GAME; FRACTALS; ORBITS; ENDOMORPHISMS; SPACES;

D O I：

10.1090/S0002-9939-2011-11105-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2575 / 2587

页数：13

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