Ryan Broderick
Published 2016-11-03Version 1
If $F$ and $G$ are iterated function systems, then any infinite word $W$ in the symbols $F$ and $G$ induces a limit set. It is natural to ask whether this Cantor set can also be realized as the limit set of a single $C^{1 + \alpha}$ iterated function system $H$. We prove that under certain assumptions on $F$ and $G$, the answer is no. This problem is motivated by the spectral theory of one-dimensional quasicrystals.
The Cantor set of linear orders on N is the universal minimal S_\infty-system
On the union of middle-$(1-2β)$ Cantor set with its translations
On the size of attractors in $\mathbb{CP}^k$
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