Analysis on self-similar sets

Date

2020-08

Editor(s)

Advisor

Gheondea E., Aurelian B. N.

Supervisor

Co-Advisor

Co-Supervisor

Instructor

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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.

Source Title

Publisher

Course

Other identifiers

Book Title

Degree Discipline

Mathematics

Degree Level

Master's

Degree Name

MS (Master of Science)

Citation

Published Version (Please cite this version)

Language

English

Type