Graduation Year
2026
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Reader 1
Stephan Garcia
Reader 2
Winston Ou
Terms of Use & License Information
This work is licensed under a Creative Commons Attribution 4.0 License.
Rights Information
2026 Anne D Bannon
Abstract
This thesis is intended to provide a comprehensive overview of the literature required to fully understand research conducted during the University of Connecticut's Fractals & Stochastics REU in the summer of 2025. The literature review includes a description of Robert Strichartz's seminal work pertaining to the Laplacian spectrum of the Sierpiński Gasket, which provides a framework for how we approach studying the spectrum of the basilica Julia set. Defining the basilica Julia set and the closely-related Basilica group involves graph theory, automata theory, iterated monodromy group theory, and amenable group theory. Further time is dedicated to defining the graph Laplacian and surveying its most salient properties. In the research itself, we study the spectral properties of a sequence of weighted Schreier graphs of the Basilica group, which approximate the basilica Julia set in the limit space. We develop a novel dynamical system describing the behavior of the Laplacian eigenvalues and use those dynamics to study associated eigenfunctions. This thesis concludes with a list of potential directions for future research and a brief personal reflection.
Recommended Citation
Bannon, Anne D., "Spectral Decimation on the Schreier Graphs of the Basilica Group: A Thesis in Fractal Analysis" (2026). Scripps Senior Theses. 2730.
https://scholarship.claremont.edu/scripps_theses/2730
