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From the same journal

On shrinking targets for Z^m actions on tori

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Publication details

DatePublished - Jul 2010
Issue number2
Number of pages10
Pages (from-to)193-202
Original languageEnglish


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.

    Research areas

  • Number Theory


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