Laplacians on a family of quadratic Julia Sets
This page (still somewhat under construction) displays the work done in summer 2008 at Cornell University on Laplacians on Julia Sets. We use the methods of graph (inner) approximation to construct discrete approximations to two Lapcians on quasicircles, the Bascilica and Douady's Rabbit. We then study the spectra of these Laplacians using matlab's linear algebra routines.
- Data: numerical approximations to our constructed Laplacians on Quasicircles, the Basilica, and Douady's Rabbit.
- Exceptional Eigenfunctions: A few examples from the data that defy simple explanation.
- Download the matlab code used to produce the data.
- A note about the approximation of Hausdorff dimension
- Additions, Corrections or Feedback on this page to:
- tflock @ "remove this" math dot berkeley dot edu
- Additional acknowledgements:
- Bob Strichartz, Steven Heilman, Miles Wheeler, Yingying Chan, Sarah Constantin, Steve Gaarder, Russ Thompson
Last Update: 5 June 2009