Transmission fingerprints of quasi-periodic chains

We propose a method to characterize quasi-periodic chains, based on the transmission probabilities. We consider finite layers which are building up following the Fibonaci, Thue-Morse and Cantor sequences. The spectra show an undoubtedly fractal behavior, with a distinct appearence for each chain. Furthermore, we construct return maps which present the same characteristic attractor for all peaks of energies within the same kind of chain.