seminar: Unique and simultaneous codings for self-similar sets
speaker: Karma Dajani (Universiteit Utrecht)abstract: Our goal is to study unique and simultaneous codings generated by special classes of iterated function system consisting of contracting lines. We first consider the case where the attractor K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence of this, we can show that the set of unique codings is a graph-directed self-similar set in the sense of Mauldin and Williams. The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of this set. Secondly, we consider IFS generating codings representing simultaneously two different points in two different bases. We show that for bases sufficiently close to 1 , the attractor contains a neighbourhood of the origin.
timetable:
Tue 14 Apr, 16:00 - 17:30, Dipartimento di Matematica
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