Quasicircle Equilibrium Measure Spectra
We can have numerical results for graph levels 2-12. This page contains eigenvalue tables including all levels and pictures of the eigenfunctions for the level 6-10 approximations.
The highlights of our findings:
Equilibrium measure reproduces the standard results from the circle.
- Here is a table of eigenvalues ( unnormalized | normalized).
- Predictions: Using the calculated eigenvalues on level 2-13 we predict the eigenvalues in the limit that the level goes to infinity using differences between successive levels and the ratios between them.
- Note: the little question marks are an artifact of transferring my Excel file to HTML, not a comment on the data.
- Using the prediction described above we get pictures of the eigenvalue counting function and Weyl ratio.
- Here are pictures of eigenfunctions on level 6-10. Eigenfunctions up to 256 where available are shown. 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.
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Last Update: 2 June 2009