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Stable iterated function systemsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 1992 (English)Doctoral thesis, monograph (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Umeå: Umeå universitet , 1992. , 70 p.
##### Series

Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 4
##### Keyword [en]

Hausdorff metric, iterated function system (IFS), attractor, invariant set, address, Hutchinson’s metric, we a k* -topology, IFS with probabilities, invariant measure, the Random Iteration Algorithm
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-100370ISBN: 91-7174-688-9OAI: oai:DiVA.org:umu-100370DiVA: diva2:792091
##### Public defence

1992-06-01, Hörsal A, Samhällsvetarhuset, Umeå universitet, Umeå, 10:15
#####

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##### Supervisors

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#####

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##### Projects

digitalisering@umu
##### Note

The purpose of this thesis is to generalize the growing theory of *iterated function systems *(IFSs). Earlier, *hyperbolic *IFSs with finitely many functions have been studied extensively. Also, hyperbolic IFSs with infinitely many functions have been studied. In this thesis, more general IFSs are studied.

The *Hausdorff pseudometric *is studied. This is a generalization of the Hausdorff metric. Wide *and narrow limit sets *are studied. These are two types of limits of sequences of sets in a complete pseudometric space.

*Stable Iterated Function Systems*, a kind of generalization of hyperbolic IFSs, are defined. Some different, but closely related, types of stability for the IFSs are considered. It is proved that the IFSs with the most general type of stability have unique attractors. Also, invariant sets, addressing, and periodic points for stable IFSs are studied.

Hutchinson’s metric (also called Vaserhstein’s metric) is generalized from being defined on a space of probability measures, into a class of norms, the £-norms, on a space of *real measures *(on certain metric spaces). Under rather general conditions, it is proved that these norms, when they are restricted to positive measures, give rise to complete metric spaces with the metric topology coinciding with the *weak**-topology.

Then, IFSs with probabilities (IFSPs) are studied, in particular, stable IFSPs. The £-norm-results are used to prove that, as in the case of hyperbolic IFSPs, IFSPs with the most general kind of stability have unique invariant measures. These measures are ”attractive”. Also, an invariant measure is constructed by first ”lifting” the IFSP to the code space. Finally, it is proved that the Random Iteration Algorithm in a sense will ”work” for some stable IFSPs.

Diss. Umeå : Umeå universitet, 1992

Available from: 2015-03-03 Created: 2015-03-02 Last updated: 2015-04-08Bibliographically approvedReferences$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1120",{id:"formSmash:lower:j_idt1120",widgetVar:"widget_formSmash_lower_j_idt1120",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1121_j_idt1123",{id:"formSmash:lower:j_idt1121:j_idt1123",widgetVar:"widget_formSmash_lower_j_idt1121_j_idt1123",target:"formSmash:lower:j_idt1121:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});