English

Attractors of sequences of iterated function systems

Dynamical Systems 2018-03-07 v4

Abstract

If FF and GG are iterated function systems, then any infinite word WW in the symbols FF and GG induces a limit set. It is natural to ask whether this Cantor set can also be realized as the limit set of a single C1+αC^{1 + \alpha} iterated function system HH. We prove that under certain assumptions on FF, GG and HH, the answer is no. This problem is motivated by the spectral theory of one-dimensional quasicrystals.

Cite

@article{arxiv.1611.01196,
  title  = {Attractors of sequences of iterated function systems},
  author = {Ryan Broderick},
  journal= {arXiv preprint arXiv:1611.01196},
  year   = {2018}
}
R2 v1 2026-06-22T16:41:37.280Z