Projects per year
Abstract
Let A be an n×m matrix with real entries. Consider the set BadA of x[0,1)n for which there exists a constant c(x)>0 such that for any qm the distance between x and the point {A q} is at least c(x)qm/n. It is shown that the intersection of BadA with any suitably regular fractal set is of maximal Hausdorff dimension. The linear form systems investigated in this paper are natural extensions of irrational rotations of the circle. Even in the latter onedimensional case, the results obtained are new.
Original language  English 

Pages (fromto)  193202 
Number of pages  10 
Journal  Mathematika 
Volume  56 
Issue number  2 
DOIs  
Publication status  Published  Jul 2010 
Keywords
 Number Theory
Projects
 2 Finished

Classical metric Diophantine approximation revisited
24/03/08 → 23/07/11
Project: Research project (funded) › Research

Inhomogenous approximation on manifolds
15/02/08 → 14/04/11
Project: Research project (funded) › Research