Period-adding sequences and their scaling in a multiple devil's staircase

摘要

We have discovered a multiple Devil's staircase that loses both self-similarity and monotonicity, in an 1-d piece-wise smooth map and analytically obtained the parameter positions of the end points of each phase-locked steps, and also found the scaling laws of the period-adding sequences that construct the staircase. These scaling laws are very different from the period-adding sequences in conventional Devil's staircases.