Electrical networks on n-simplex fractals

The decimation map D for a network of admittances on an n- simplex lattice fractal is studied. The asymptotic behaviour of D for large- size fractals is examined. It is found that in the vicinity of the isotropic point the eigenspaces of the linearized map are always three for n >= 4; they are given a characterization in terms of graph theory. A new anisotropy exponent, related to the third eigenspace, is found, with a value crossing over from ln[(n + 2)/3]/ln 2 to ln[(n + 2)(3)/n(n + 1)(2)]/ln 2.