Multi-rotations on the unit circle
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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.
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
Journal of Number Theory
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
DescriptionHY was financially supported by the University of St Andrews.
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