The complexity of the set of codings for self-similar sets
speaker: Simon Baker (University of Warwick)abstract: In this talk I will discuss a recent paper with Derong Kong where we study the complexity of the set of codings for self-similar sets. In this paper we prove that if the similarities in our iterated function system have contraction ratios sufficiently close to 1, then every interior point of the attractor has a coding containing all finite words. Similarly we prove that for any positive integer k, if the similarities in our iterated function system have contraction ratios sufficiently close to 1 (in a way that depends upon k), then every interior point of the attractor has a coding such that all blocks of length k occur with the same frequency. Our arguments make use of a well known construction of a normal number due to Champernowne, and techniques due to Erdos and Komornik.
timetable:
Thu 13 Dec, 16:00 - 16:45, Aula Dini
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