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dc.contributor.authorYu, Han
dc.date.accessioned2020-01-17T00:34:51Z
dc.date.available2020-01-17T00:34:51Z
dc.date.issued2019-07
dc.identifier.citationYu , H 2019 , ' Multi-rotations on the unit circle ' , Journal of Number Theory , vol. 200 , pp. 316-328 . https://doi.org/10.1016/j.jnt.2018.12.008en
dc.identifier.issn0022-314X
dc.identifier.otherPURE: 257445163
dc.identifier.otherPURE UUID: d5182c30-f6af-40f2-a754-f9d8db8e0f8c
dc.identifier.otherRIS: urn:97B3D4527456A1371C49BAF0DCE31B9F
dc.identifier.otherScopus: 85060308010
dc.identifier.otherWOS: 000462809100010
dc.identifier.urihttp://hdl.handle.net/10023/19296
dc.descriptionHY was financially supported by the University of St Andrews.en
dc.description.abstractIn 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.
dc.language.isoeng
dc.relation.ispartofJournal of Number Theoryen
dc.rightsCopyright © 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.2018.12.008en
dc.subjectMulti-rotation orbitsen
dc.subjectαβ-setsen
dc.subjectRecurrent sequencesen
dc.subjectDiophantine approximation on linear formsen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleMulti-rotations on the unit circleen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1016/j.jnt.2018.12.008
dc.description.statusPeer revieweden
dc.date.embargoedUntil2020-01-17
dc.identifier.urlhttps://arxiv.org/abs/1808.09911en


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