Parameter Families of Iterated Function Systems and Continuity

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dc.creatorMurphy, Maxwell
dc.date2006-08-22
dc.date.accessioned2026-07-07T07:22:02Z
dc.date.available2026-07-07T07:22:02Z
dc.descriptionIn 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.
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/math/0608552
dc.identifierhttp://arxiv.org/abs/math/0608552
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115518
dc.subjectDynamical Systems
dc.subject28A80
dc.titleParameter Families of Iterated Function Systems and Continuity
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