Explicit orbits for renormalization maps for Green functions on fractal lattices.

Abstract

Renormalization recursions for Schrodinger Green functions on several fractal lattices are solved explicitly in the sense in which one solves a system of difference equations. In other words, explicit orbits are constructed for the dynamical systems corresponding to the rational, planar maps that comprise the renormalization recursions. This construction is possible for each energy in the Cantor set of the infinite lattice spectrum. Thus if i and j are sites on opposite corners of the lattice the Green functions x=G ii and y=G ij are obtained as closed formulas as a function of lattice size L for fixed energy