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Parameter Families of Iterated Function Systems and Continuity

Maxwell Murphy
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Abstract

In this paper, we investigate parameter families of iterated function systems and continuity. Specifically, if we have a set of iterated function systems that depend continuously on a parameter, which properties of the invariant sets will vary continuously? We show here that the invariant sets will vary continuously as a function of the parameter. Furthermore, we give some sufficient conditions under which the Hausdorff dimension will depend continuously on the parameter. Lastly, we give a counter-example where the dimension is not a continuous function of the parameter.

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Maxwell Murphy. 2006-08-22. Parameter Families of Iterated Function Systems and Continuity. https://arxiv.org/abs/math/0608552

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