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On shrinking targets for Z^m actions on tori
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| Journal | Mathematika |
|---|---|
| Date | Published - Jul 2010 |
| Issue number | 2 |
| Volume | 56 |
| Number of pages | 10 |
| Pages (from-to) | 193-202 |
| Original language | English |
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)|q|-m/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 one-dimensional case, the results obtained are new.
- Number Theory
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Project: Research project (funded) › Research
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