Abstract
Let Tx = x + θ (mod 1). Define Kn(x, y) = min{j ≥ 1 : Tjy ∈. Qn(x)}, where Qn(x) = [2 -ni,2-n(i + 1)) for 2-ni ≤ x < 2 -n(i + 1). Then for irrational θ of type η lim inf n→∞log Kn(x, y)/n = 1 a.e., lim sup n→∞log Kn(x, y)/n = η a.e. Since the set of irrational numbers of type 1 has measure 1, for almost every 9 the limit exists and is 1.
Original language | English |
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Pages (from-to) | 1861-1868 |
Number of pages | 8 |
Journal | Nonlinearity |
Volume | 16 |
Issue number | 5 |
DOIs | |
State | Published - Sep 2003 |