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Badly approximable numbers and vectors in Cantor-like sets

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.

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Official URL: http://www.ams.org/journals/proc/2012-140-08/S0002...

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
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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