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### Bibtex

@techreport{29c74310dbd311dd9710000ea68e967b,

title = "On shrinking targets for Zm actions on tori",

abstract = "Let be an matrix with real entries. Consider the set of for which there exists a constant 0${"} style={"}vertical-align: middle; border-width: 0px{"}/> such that for any the distance between and the point is at least . It is shown that the intersection of 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.",

author = "Yann Bugeaud and Stephen Harrap and S. Kristensen and Sanju Velani",

year = "2008",

pages = "1--12",

publisher = "Department of Mathematical Sciences, Aarhus University",

type = "WorkingPaper",

institution = "Department of Mathematical Sciences, Aarhus University",

}

### RIS

TY - UNPB

T1 - On shrinking targets for Zm actions on tori

AU - Bugeaud,Yann

AU - Harrap,Stephen

AU - Kristensen,S.

AU - Velani,Sanju

PY - 2008

Y1 - 2008

N2 - Let be an matrix with real entries. Consider the set of for which there exists a constant 0$" style="vertical-align: middle; border-width: 0px"/> such that for any the distance between and the point is at least . It is shown that the intersection of 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.

AB - Let be an matrix with real entries. Consider the set of for which there exists a constant 0$" style="vertical-align: middle; border-width: 0px"/> such that for any the distance between and the point is at least . It is shown that the intersection of 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.

M3 - Working paper

SP - 1

EP - 12

BT - On shrinking targets for Zm actions on tori

PB - Department of Mathematical Sciences, Aarhus University

ER -