Eigenvalue Algorithm for Hausdorff Dimension on Complex Kleinian Groups

Authors

Jacob Linden, University of WashingtonFollow
Xuqing Wu, University of WashingtonFollow

Abstract

In this manuscript, we present computational results approximating the Hausdorff dimension for the limit sets of complex Kleinian groups. We apply McMullen's eigenvalue algorithm \cite{mcmullen} in symmetric and non-symmetric examples of complex Kleinian groups, arising in both real and complex hyperbolic space. Numerical results are compared with asymptotic estimates in each case. Python code used to obtain all results and figures can be found at \url{https://github.com/WXML-HausDim/WXML-project}, all of which took only minutes to run on a personal computer.

Author Bio

Jacob Linden is a senior at the University of Washington majoring in Applied and Computational Mathematical Sciences. His mathematical interests lie primarily in differential equations, dynamical systems, and algorithms. In the fall, he will be joining the University of Chicago in pursuit of a PhD in applied mathematics.

Xuqing Wu is a senior at the University of Washington, double majoring in Applied and Computational Mathematical Sciences and Economics. Specializing in econometric and statistical modeling, Xuqing aims to be a data analyst who could provide decisive information for multinationals. Later this year she will go to graduate school to further her study of applied statistics.

Faculty Sponsor

Hadrian Quan

Recommended Citation

Linden, Jacob and Wu, Xuqing (2023) "Eigenvalue Algorithm for Hausdorff Dimension on Complex Kleinian Groups," Rose-Hulman Undergraduate Mathematics Journal: Vol. 24: Iss. 2, Article 12.
Available at: https://scholar.rose-hulman.edu/rhumj/vol24/iss2/12