Scaling properties of a structure intermediate between quasiperiodic and random

@article{Aubry1988ScalingPO,
  title={Scaling properties of a structure intermediate between quasiperiodic and random},
  author={S. Aubry and Claude Godr{\`e}che and Jean-Marc Luck},
  journal={Journal of Statistical Physics},
  year={1988},
  volume={51},
  pages={1033-1075}
}
We consider a one-dimensional structure obtained by stringing two types of “beads” (short and long bonds) on a line according to a quasiperiodic rule. This model exhibits a new kind of order, intermediate between quasiperiodic and random, with a singular continuous Fourier transform (i.e., neither Dirac peaks nor a smooth structure factor). By means of an exact renormalization transformation acting on the two-parameter family of circle maps that defines the model, we study in a quantitative way… 
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