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On Hausdorff type distances and their application to fractals

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dc.contributor.advisor Bartoszek WK, Prof en
dc.contributor.advisor Alderton IW, Prof en
dc.contributor.author Moshokoa SP en
dc.date.accessioned 2016-09-22T11:53:30Z
dc.date.available 2016-09-22T11:53:30Z
dc.date.created 1999 en
dc.date.submitted 2000 en
dc.identifier.uri http://hdl.handle.net/20.500.11892/140697
dc.description.abstract We first define the Hausdorff metric d on the set of real numbers, the space of all nonempty compact subsets of the metric space. We discuss some of the properties that (the set of real numbers, d) inherits from (X, &rho;), for instance completeness and compactness. In particular when (X, &rho;) is complete, we define the Barnsley operator F : the set of real numbers -> the set of real numbers in terms of the associated iterated function systems {S<sub>i</sub> : X - X : i is an element of a set I}. We discuss the properties of the Barnsley operator by using the Banach contraction principle when the iterated function systems is hyperbolic. We generalize our theory by defining a metric dist on T, the space of all nonempty closed (unbounded) subsets of (X, &rho;), and discuss convergence as well as the closed limit A of the sequence {A<sub>n</sub>} in T. We also investigate properties of the Barnsley operator F when the set {S<sub>i</sub> : X -> X : i is an element of a set 1} consists of continuous transformations, which may not be hyperbolic. en
dc.language English en
dc.subject Mathematics, mathematical statistics and statistics en
dc.subject Algebra and number theory en
dc.title On Hausdorff type distances and their application to fractals en
dc.type Masters degree en
dc.description.degree MSc en


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