Analysis on self-similar sets
| buir.advisor | Gheondea E., Aurelian B. N. | |
| dc.contributor.author | Kesimal, Hayriye Sıla | |
| dc.date.accessioned | 2020-08-28T08:01:53Z | |
| dc.date.available | 2020-08-28T08:01:53Z | |
| dc.date.copyright | 2020-08 | |
| dc.date.issued | 2020-08 | |
| dc.date.submitted | 2020-08-14 | |
| dc.department | Department of Mathematics | en_US |
| dc.description | Cataloged from PDF version of article. | en_US |
| dc.description | Thesis (M.S.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2020. | en_US |
| dc.description | Includes bibliographical references (leaves 40-42). | en_US |
| dc.description.abstract | Self-similar sets are one class of fractals that are invariant under geometric similarities. In this thesis, we study on self-similar sets. We give the definition of a self-similar set K and present the proof the existence theorem of such a set. We define the shift space. We define a relation between the shift space and K. We show the self-similarity of the shift space. We define overlapping set, critical and post-critical set for a self-similar set. We give the characterization of K by the periodic sequences in the shift space. We give the notion of a self-similar structure and define a self-similar set purely topologically. We give its local topology. We define isomorphism between selfsimilar structures so that we can have a classification of self-similar structures. We point out that the critical set for a self-similar structure provides us with a characterization for determining the topological structure of a self-similar structure. We define the notion of minimality for a self-similar structure and give a characterization theorem for investigating the minimality of a self-similar structure. We define a post-critically finite self-similar structure. | en_US |
| dc.description.degree | M.S. | en_US |
| dc.description.statementofresponsibility | by Hayriye Sıla Kesimal | en_US |
| dc.format.extent | viii, 42 leaves : charts ; 30 cm. | en_US |
| dc.identifier.itemid | B154068 | |
| dc.identifier.uri | http://hdl.handle.net/11693/53963 | |
| dc.language.iso | English | en_US |
| dc.publisher | Bilkent University | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Self-similar set | en_US |
| dc.subject | Shift space | en_US |
| dc.subject | Shift map | en_US |
| dc.subject | Critical set | en_US |
| dc.subject | Post-critical set | en_US |
| dc.subject | Self-similar structure | en_US |
| dc.subject | Post-critically finite set | en_US |
| dc.title | Analysis on self-similar sets | en_US |
| dc.title.alternative | Kendine benzer kümeler üzerinde analiz | en_US |
| dc.type | Thesis | en_US |