Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Keyword
- Publication
- Publication Type
Articles 1 - 2 of 2
Full-Text Articles in Dynamical Systems
Eigenvalue Algorithm For Hausdorff Dimension On Complex Kleinian Groups, Jacob Linden, Xuqing Wu
Eigenvalue Algorithm For Hausdorff Dimension On Complex Kleinian Groups, Jacob Linden, Xuqing Wu
Rose-Hulman Undergraduate Mathematics Journal
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.
Applying Hallgren’S Algorithm For Solving Pell’S Equation To Finding The Irrational Slope Of The Launch Of A Billiard Ball, Sangheon Choi
Applying Hallgren’S Algorithm For Solving Pell’S Equation To Finding The Irrational Slope Of The Launch Of A Billiard Ball, Sangheon Choi
Mathematical Sciences Technical Reports (MSTR)
This thesis is an exploration of Quantum Computing applied to Pell’s equation in an attempt to find solutions to the Billiard Ball Problem. Pell’s equation is a Diophantine equation in the form of x2 − ny2 = 1, where n is a given positive nonsquare integer, and integer solutions are sought for x and y. We will be applying Hallgren’s algorithm for finding irrational periods in functions, in the context of billiard balls and their movement on a friction-less unit square billiard table. Our central research question has been the following: Given the cutting sequence of the billiard …