Main content

Attractors and Semi-Attractors of IFS

Show simple item record

dc.contributor.advisor Kunze, Herb Fitzsimmons, Maxwell 2018-12-18T18:08:41Z 2018-12-18T18:08:41Z 2018 2018-12-12 2018-12-18
dc.description.abstract It is well known that a finite set of contractive self maps on a metric space, called an iterated function system (IFS), admit a nonempty compact invariant set called the attractor of the IFS. It is also well known that the chaos game converges to "draw" the attractor. We examine generalized notions of IFSs, attractors and the convergence of the chaos game to these generalized attractors. We focus on IFSs whose Hutchinson operator is a lower semi continuous multifunction, this includes infinite and possibly discontinuous IFS. In this case we develop several characterizations of smallest/minimal nonempty closed sub-invariant sets of the IFS. Under the same assumptions, we then give some necessary conditions for the chaos game to converge. Then, under the assumption that the set of all finite compositions of functions in the IFS are equicontinuous and certain compactness assumptions, we establish that the chaos game converges. en_US
dc.language.iso en en_US
dc.publisher University of Guelph en_US
dc.subject fractals en_US
dc.subject chaos game en_US
dc.subject IFS en_US
dc.subject quasi attractor en_US
dc.subject semi attractor en_US
dc.subject multifunctions en_US
dc.title Attractors and Semi-Attractors of IFS en_US
dc.type Thesis en_US Mathematics and Statistics en_US Master of Science en_US Department of Mathematics and Statistics en_US
dc.rights.license All items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated. University of Guelph en_US

Files in this item

Files Size Format View Description
fitzsimmons_maxwell_201812_Msc.pdf 559.4Kb PDF View/Open Thesis of Maxwell Fitzsimmons

This item appears in the following Collection(s)

Show simple item record

The library is committed to ensuring that members of our user community with disabilities have equal access to our services and resources and that their dignity and independence is always respected. If you encounter a barrier and/or need an alternate format, please fill out our Library Print and Multimedia Alternate-Format Request Form. Contact us if you’d like to provide feedback:  (email address)