# Simon Kristensen

## On shrinking targets for Zm actions on tori

Research output: Working paperResearch

### Standard

On shrinking targets for Zm actions on tori. / Bugeaud, Yann; Harrap, Stephen; Kristensen, S.; Velani, Sanju.

Århus : Department of Mathematical Sciences, Aarhus University, 2008. p. 1-12.

Research output: Working paperResearch

### Harvard

Bugeaud, Y, Harrap, S, Kristensen, S & Velani, S 2008 'On shrinking targets for Zm actions on tori' Department of Mathematical Sciences, Aarhus University, Århus, pp. 1-12.

### APA

Bugeaud, Y., Harrap, S., Kristensen, S., & Velani, S. (2008). On shrinking targets for Zm actions on tori. (pp. 1-12). Århus: Department of Mathematical Sciences, Aarhus University.

### CBE

Bugeaud Y, Harrap S, Kristensen S, Velani S. 2008. On shrinking targets for Zm actions on tori. Århus: Department of Mathematical Sciences, Aarhus University. pp. 1-12.

### MLA

Bugeaud, Yann et al. On shrinking targets for Zm actions on tori. 1-12. Århus: Department of Mathematical Sciences, Aarhus University. 2008, 12 p.

### Vancouver

Bugeaud Y, Harrap S, Kristensen S, Velani S. On shrinking targets for Zm actions on tori. Århus: Department of Mathematical Sciences, Aarhus University. 2008, p. 1-12.

### Author

Bugeaud, Yann ; Harrap, Stephen ; Kristensen, S. ; Velani, Sanju. / On shrinking targets for Zm actions on tori. Århus : Department of Mathematical Sciences, Aarhus University, 2008. pp. 1-12

### Bibtex

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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", language = "English", 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

CY - Århus

ER -