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 Duady's Rabbit. We then study the spectra of these Laplacians using matlab's linear algebra routines.

• Data from our experiments
• Download the matlab code used to produce the data.
• A note about the approximation of Hausdorff dimension
• The rest of this list is a lie
• Detailed explanation of our approach to problem
• A note about outer approximation. This is another method we attempted to use to understand laplacians on these sets, however as it was less rewarding this has been discontinued, but you can view our results, code and methods here.
• Related resources including...

Additions, Corrections or Feedback on this page to:

taryn.flock@aya.yale.edu

Additional acknowledgements:

Bob Strichartz, Steven Heilman, Miles Wheeler, Yingying Chan, Sarah Constantin, Steve Gaarder, Russ Thompson

Last Update: 5 June 2009