Fractal Geometry Seminar

Wednesday, September 23, 2015 2:30 pm - 2:30 pm EDT

Anthony McCormick, Pure Math Department, University of Waterloo 

“Recent Methods for Computing the Hausdorff Dimension of a Self-Similar Set”

I will begin by discussing some results proven by Deng, Lau and Ngai regarding the relationship between the various separation conditions that have been introduced in the investigation of iterated function systems with overlap. Namely, the fact that the finite type condition implies exponential commensurability between the contraction ratios of an IFS and is therefore not implied by the open set condition in general. This motivates the definition of the generalized finite type condition which yields an algorithm for computing the Hausdorff dimension of certain IFSs similar to the one for the original FTC. Then I plan to discuss a recent construction of Deng which provides a systematic method of piecing together an infinite IFS satisfying the OSC from a finite IFS which can be partitioned into two iterated function systems satisfying the OSC with respect to the same open set.

MC 5403