Numerical Values of the Hausdorff and Packing Measures for Limit Sets of Iterated Function Systems
Description:
In the context of fractal geometry, the natural extension of volume in Euclidean space is given by Hausdorff and packing measures. These measures arise naturally in the context of iterated function systems (IFS). For example, if the IFS is finite and conformal, then the Hausdorff and packing dimensions of the limit sets agree and the corresponding Hausdorff and packing measures are positive and finite. Moreover, the map which takes the IFS to its dimension is continuous. Developing on previous …
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Date:
August 2017
Creator:
Reid, James Edward
Partner:
UNT Libraries