A note on badly approximable linear forms on manifolds

@article{Bengoechea2017ANO,
title={A note on badly approximable linear forms on manifolds},
author={P. Bengoechea and N. Moshchevitin and Natalia Stepanova},
journal={Mathematika},
year={2017},
volume={63},
pages={587-601}
}

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… CONTINUE READING