Dear all,
Tomorrow's speaker in the Analysis and Probability Seminar is Matt Shaw from the University
of Tennessee. The title of his talk is "Parametrizability of IIFS attractors."
The talk will begin at 2:30pm tomorrow in Mont 313.
Abstract: In 1985, Hata showed that whenever the attractor K of a finite iterated function
system is connected, it is the image of a curve, and if additionally it is contained in Euclidean space, then by a result of Remes from 1998 it is the image of a 1/s-Holder continuous curve, where s is the similarity dimension of the system. We show some conditions
under which the attractor of an infinite iterated function system (IIFS) is the image of a curve, or the image of a Holder continuous curve. If time permits, we will also provide examples of compact and connected attractors of IIFS in the plane; one which
is not the image of a curve, and one which is the image of a curve but not the image of any Holder continuous curve.
Best,
Sean
