Kurzweil type metrical Diophantine properties in the field of formal Laurent series

Dong Han Kim; Bo Tan; Baowei Wang; Jian Xu

doi:10.1016/j.jmaa.2013.05.023

Kurzweil type metrical Diophantine properties in the field of formal Laurent series

Dong Han Kim
, Bo Tan
, Baowei Wang
, Jian Xu

Department of Mathematics Education

Huazhong University of Science and Technology

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this article, we consider Diophantine properties of the orbit of irrational rotations over the field of formal Laurent series Fq((X-1)). More precisely, for a given f∈Fq((X-1)) and a sequence (r_n), we investigate the size of the set {g∈Fq((X-1)):mindegQ=n|{Qf}-g|<rn forinfinitelymanyn∈N} in the sense of the Haar measure and the Hausdorff dimension.

Original language	English
Pages (from-to)	250-262
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	407
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2013.05.023
State	Published - 15 Nov 2013

Keywords

Formal Laurent series
Hausdorff dimension
Inhomogeneous Diophantine approximation

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10.1016/j.jmaa.2013.05.023

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abstract = "In this article, we consider Diophantine properties of the orbit of irrational rotations over the field of formal Laurent series Fq((X-1)). More precisely, for a given f∈Fq((X-1)) and a sequence (rn), we investigate the size of the set \{g∈Fq((X-1)):mindegQ=n|\{Qf\}-g|",

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AU - Kim, Dong Han

AU - Tan, Bo

AU - Wang, Baowei

AU - Xu, Jian

PY - 2013/11/15

Y1 - 2013/11/15

N2 - In this article, we consider Diophantine properties of the orbit of irrational rotations over the field of formal Laurent series Fq((X-1)). More precisely, for a given f∈Fq((X-1)) and a sequence (rn), we investigate the size of the set {g∈Fq((X-1)):mindegQ=n|{Qf}-g|

AB - In this article, we consider Diophantine properties of the orbit of irrational rotations over the field of formal Laurent series Fq((X-1)). More precisely, for a given f∈Fq((X-1)) and a sequence (rn), we investigate the size of the set {g∈Fq((X-1)):mindegQ=n|{Qf}-g|

KW - Formal Laurent series

KW - Hausdorff dimension

KW - Inhomogeneous Diophantine approximation

UR - https://www.scopus.com/pages/publications/84879786363

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SP - 250

EP - 262

JO - Journal of Mathematical Analysis and Applications

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IS - 2

ER -

Kurzweil type metrical Diophantine properties in the field of formal Laurent series

Abstract

Keywords

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