Resistance of one-dimensional quasicrystals

One-dimensional quasiperiodic systems are often based on an inflation rule giving rise to a recursion formula on the transfer matrices. It is shown in a general setting, that the norm growth of these matrices can be evaluated. A consequence is, for instance, a purely critical regime (namely polynomial bounds in function of the sample size) for the electrical resistance, when the energy is in the spectrum. This solves a conjecture by Sutherland and Kohmoto.