Multi-rotations on the unit circle

Han Yu

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
5 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)316-328
JournalJournal of Number Theory
Early online date17 Jan 2019
Publication statusPublished - Jul 2019


  • Multi-rotation orbits
  • αβ-sets
  • Recurrent sequences
  • Diophantine approximation on linear forms


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