Attractors of sequences of iterated function systems. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Broderick, Ryan
• Is Part Of: Dynamical systems. Volume 34:Issue 1(2019)
• Page Start: 40
• Page End: 52
• Publication Date: 2019-01-02
• Subjects: Iterated function systems; 28A80; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2018.1450358
• Languages: English
• ISSNs: 1468-9367

Abstract

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.