On the refined shrinking target property of rotations

2012/01/22 by Kim, Dong Han · 1 citation
#11J83 #11K60 #37E10 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1201.4568

Abstract

We discuss the shrinking target property of irrational rotations. We obtain the condition of an irrational θ and monotone increasing φ(n) such that \liminf_{n → ∞} n φ(n) ‖ nθ- s ‖ = 0 for almost every s. We also consider the class of irrationals for which the limit inferior is 0 for every monotone increasing φ(n) such that ∑_n 1/(nφ(n)) diverges.

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