All ETDs from UAB

Advisory Committee Chair

John C Mayer

Advisory Committee Members

Nikita Selinger

Mahmut Unan

Document Type


Date of Award


Degree Name by School

Master of Science (MS) College of Arts and Sciences


Laminations are a combinatorial and topological model for studying the Julia sets of complex polynomials. Every complex polynomial of degree d has d fixed points counted with multiplicity. From the point of view of laminations, exactly d−1 of these fixed points are peripheral (approachable from outside the Julia set of the polynomial). Hence, at least one of the d fixed points is “hidden” from the laminational point of view. The purpose of this thesis is to identify, classify and count the possible fixed point portraits for any lamination of degree d. We will identify the “simplest” lamination for a given fixed point portrait and will show that there are polynomials that have these simplest laminations. We extend σd to D as a branched covering map. In future work with others, we want to apply Thurston’s criterion to show there exists a complex polynomial whose lamination this is.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.