Scaling Properties of the Period-Adding Sequences in a Multiple Devil’s Staircase

In this letter the scaling properties of the period-adding sequences in a so-called “multiple Devil’s staircase” are reported. It is certified both analytically and numerically that the width of the i-th phase-locked plateau in a sequence scales as In |Δe(i)| ∝ i, and the position of the plateau scales as In |e_∞ -e_i| ∝ i. These properties are qualitatively different from those of the period-adding sequences in conventional Devil’s staircases.