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.Full text not available from this repository.
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|
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