Dani, SG and Shah, Hemangi
(2012)
*Badly approximable numbers and vectors in Cantor-like sets.*
In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 140
(8).
pp. 2575-2587.

## Abstract

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.

Item Type: | Journal Article |
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Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 17 Aug 2012 06:52 |

Last Modified: | 17 Aug 2012 06:52 |

URI: | http://eprints.iisc.ernet.in/id/eprint/44942 |

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