Sierpiński Fractals and the Dimension of Their Laplacian Spectrum

Abstract

We establish rigorous estimates for the Hausdorff dimension of the spectra of Laplacians associated with Sierpiński lattices and infinite Sierpiński gaskets and other post-critically finite self-similar sets.

Keywords

• Laplacian spectrum
• Sierpiński Fractals
• Hausdorff dimension
• transfer operator
• Lagrange-Chebyshev interpolation