Multi-rotations on the unit circle
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
ISSN
0022-314XType
Journal article
Description
HY was financially supported by the University of St Andrews.Collections
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