Abstract
The decimation map for a network of admittances on an n-simplex lattice fractal is studied. The asymptotic behaviour of 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 to ln[(n + 2)3/n(n + 1)2]/ln 2.
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