Attractors of sequences of iterated function systems. Issue 1 (2nd January 2019) - Broderick, Ryan
ABSTRACT: IfF andG are iterated function systems, then any infinite wordW in the symbolsF andG induces a limit set. It is natural to ask whether this Cantor set can also be realized as the limit set of a single iterated function systemH . We prove that ifF, G, andH consist of C 1 + α diffeomorphisms, then under some additional constraints onF andG the answer is no. This problem is motivated by the spectral theory of one-dimensional quasicrystals.