Projects per year
Abstract
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 nondegenerate 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.
Original language  English 

Journal  Mathematika 
Early online date  11 May 2017 
Publication status  Epub ahead of print  11 May 2017 
Keywords
 math.NT
Projects
 1 Finished

Programme GrantNew Frameworks in metric Number Theory
1/06/12 → 30/11/18
Project: Research project (funded) › Research