On badly approximable complex numbers

Rune Esdahl-Schou; S. Kristensen

On badly approximable complex numbers

Research output: Working paper/Preprint › Working paper › Research

Abstract

We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably regular fractal set.

Original language	English
Place of publication	Århus
Publisher	Department of Mathematical Sciences, Aarhus University
Number of pages	8
Publication status	Published - 2009

Access to Document

http://www.imf.au.dk/publs?id=700

Cite this

@techreport{4917664947d94b7280aae7754fd24817,

title = "On badly approximable complex numbers",

abstract = "We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably regular fractal set.",

author = "Rune Esdahl-Schou and S. Kristensen",

year = "2009",

language = "English",

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

address = "Denmark",

type = "WorkingPaper",

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

}

TY - UNPB

T1 - On badly approximable complex numbers

AU - Esdahl-Schou, Rune

AU - Kristensen, S.

PY - 2009

Y1 - 2009

N2 - We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably regular fractal set.

AB - We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably regular fractal set.

M3 - Working paper

BT - On badly approximable complex numbers

PB - Department of Mathematical Sciences, Aarhus University

CY - Århus

ER -

On badly approximable complex numbers

Abstract

Access to Document

Fingerprint

Cite this