On discontinuity and tail behaviours of the integrated density of states for nested pre-fractals

We consider a general finitely ramified fractal set called a nested fractal which is determined byN number of similitudes. Basic properties of the integrated density of statesN(x) for the discrete Laplacian on the associated nested prefractal are investigated. In particulardN is shown to be purely discontinuous ifM, whereM is the number of branches of the inverse of the rational function involved in the spectral decimation method due to Rammal-Toulouse. Sierpinski gaskets and the modified Koch curve are special examples.