Abstract
In this study we discuss the shrinking target property of irrational rotations. We obtain the condition of an irrational θ and monotonically increasing φ(n) such that lim inf n → ∞ n φ (n)∥ nθ - s∥ o for almost every s.We also consider the class of irrationals for which the limit inferior is 0 for every monotonically increasing φ(n) such that ∑n 1/(nφ(n)) diverges.
| Original language | English |
|---|---|
| Pages (from-to) | 1985-1997 |
| Number of pages | 13 |
| Journal | Nonlinearity |
| Volume | 27 |
| Issue number | 9 |
| DOIs | |
| State | Published - 1 Sep 2014 |
Keywords
- irrational rotation
- metric inhomogeneous diophantine approximation
- shrinking target property