St Andrews Research Repository

St Andrews University Home
View Item 
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  •   St Andrews Research Repository
  • University of St Andrews Research
  • University of St Andrews Research
  • University of St Andrews Research
  • View Item
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.

Multi-rotations on the unit circle

Thumbnail
View/Open
Yu_2019_JNT_Multi_rotations_AAM.pdf (229.6Kb)
Date
07/2019
Author
Yu, Han
Keywords
Multi-rotation orbits
αβ-sets
Recurrent sequences
Diophantine approximation on linear forms
QA Mathematics
T-NDAS
Metadata
Show full item record
Altmetrics Handle Statistics
Altmetrics DOI Statistics
Abstract
In this paper, we study multi-rotation orbits on the unit circle. We obtain a natural generalization of a classical result which says that orbits of irrational rotations on the unit circle are dense. It is possible to show that this result holds true if instead of iterating a single irrational rotation, one takes a multi-rotation orbit along a finitely recurrent sequence over finitely many different irrational rotations. We also discuss some connections between the box dimensions of multi-rotation orbits and Diophantine approximations. In particular, we improve a result by Feng and Xiong in the case when the rotation parameters are algebraic numbers.
Citation
Yu , H 2019 , ' Multi-rotations on the unit circle ' , Journal of Number Theory , vol. 200 , pp. 316-328 . https://doi.org/10.1016/j.jnt.2018.12.008
Publication
Journal of Number Theory
Status
Peer reviewed
DOI
https://doi.org/10.1016/j.jnt.2018.12.008
ISSN
0022-314X
Type
Journal article
Rights
Copyright © 2019 Elsevier Inc. All rights reserved. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jnt.2018.12.008
Description
HY was financially supported by the University of St Andrews.
Collections
  • University of St Andrews Research
URL
https://arxiv.org/abs/1808.09911
URI
http://hdl.handle.net/10023/19296

Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

Advanced Search

Browse

All of RepositoryCommunities & CollectionsBy Issue DateNamesTitlesSubjectsClassificationTypeFunderThis CollectionBy Issue DateNamesTitlesSubjectsClassificationTypeFunder

My Account

Login

Open Access

To find out how you can benefit from open access to research, see our library web pages and Open Access blog. For open access help contact: openaccess@st-andrews.ac.uk.

Accessibility

Read our Accessibility statement.

How to submit research papers

The full text of research papers can be submitted to the repository via Pure, the University's research information system. For help see our guide: How to deposit in Pure.

Electronic thesis deposit

Help with deposit.

Repository help

For repository help contact: Digital-Repository@st-andrews.ac.uk.

Give Feedback

Cookie policy

This site may use cookies. Please see Terms and Conditions.

Usage statistics

COUNTER-compliant statistics on downloads from the repository are available from the IRUS-UK Service. Contact us for information.

© University of St Andrews Library

University of St Andrews is a charity registered in Scotland, No SC013532.

  • Facebook
  • Twitter