Conformal Measure Spectra for Douady's Rabbit
We give numerical results for Douady's Rabbit (c=.122+.745i). This page contains eigenvalue tables and pictures of the eigenfunctions.
The highlights of our findings:
This spectrum lacks much of the structure of the equilibrium measure. These results lack the expected symmetry, likely this is due to numerical error caused by the wide range of values in conformal measure approximation.
- Here is a table of eigenvalues( unnormalized | normalized).
- Using the first 256 calculated eigenvalues on level 11 we get pictures of the eigenvalue counting function and Weyl ratio.
- Here are pictures of eigenfunctions on level 6-10. The first 256 eigenfunctions are shown where available. Each row of pictures corresponds to a single eigenfunction, the first column is the ray angle description of the function, the second is the support of function colored by the sign of function, the third shows the restriction of the function to the inner circle.
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Last Update: 1 June 2009