A note on badly approximable linear forms on manifolds

TY - JOUR

T1 - A note on badly approximable linear forms on manifolds

AU - Bengoechea, Paloma

AU - Moshchevitin, Nikolay

AU - Stepanova, Natalia

PY - 2017/5/11

Y1 - 2017/5/11

N2 - This paper is motivated by Davenport's problem and the subsequent work regarding badly approximable points in submanifolds of a Euclidian 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.

AB - This paper is motivated by Davenport's problem and the subsequent work regarding badly approximable points in submanifolds of a Euclidian 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.

KW - math.NT

M3 - Article

SN - 0025-5793

JO - Mathematika

JF - Mathematika

ER -