A NOTE ON BADLY APPROXIMABLE LINEAR FORMS ON MANIFOLDS. Issue 2 (11th May 2017)

• Record Type: Journal Article
• Authors: Bengoechea, Paloma; Moshchevitin, Nikolay; Stepanova, Natalia
• Is Part Of: Mathematika. Volume 63:Issue 2(2017)
• Page Start: 587
• Page End: 601
• Publication Date: 2017-05-11
• Subjects: 11J13 -- 11J83 -- 11K60 (primary); Mathematics -- Periodicals; 510.5
• DOI: 10.1112/S0025579317000080
• Languages: English
• ISSNs: 0025-5793

Abstract

Abstract : This paper is motivated by Davenport's problem and the subsequent work regarding badly approximable points in submanifolds of a Euclidean space. We study the problem in the area of twisted Diophantine approximation and present two different approaches. The first approach shows that, under a certain restriction, any countable intersection of the sets of weighted badly approximable points on any non‐degenerate C 1 submanifold of R n has full dimension. In the second approach, we introduce the property of isotropically winning and show that the sets of weighted badly approximable points are isotropically winning under the same restriction as above.