Let α = {An}n≥1 be a sequence of left-open and right-closed intervals which partition (0, 1]. The α-Lüroth transformation Lα is defined as an infinite piecewise linear map which maps An linearly onto (0, 1] for every n ≥ 1. Then every point x ∈ (0, 1] is attached with a finite or infinite integer sequence {ℓn}n≥1 by looking at the coding of its trajectory. In this note, we consider the size of the recurrent set in such a system. More precisely, let x0 ∈(0, 1] with an infinite α-Lüroth expansion, and {tn}n≥1 an arbitrary non-decreas...
