2018/08/29 by Yu, Han
#11B30 #28A80 #37C45 #Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1808.09911
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.