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arXiv · 1611.01196

Attractors of sequences of iterated function systems

Ryan Broderick
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Abstract

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 $F$, $G$ and $H$, the answer is no. This problem is motivated by the spectral theory of one-dimensional quasicrystals.

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Ryan Broderick. 2016-11-03. Attractors of sequences of iterated function systems. https://arxiv.org/abs/1611.01196

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