| Abstract: | The topological attributes of quasiperiodic chains are revisited. The Fibonacci chain example is analyzed using the scattering of waves. Chern numbers, known to label the dense set of spectral gaps, are shown to result from an underlying (structural)palindromic symmetry. These spectral topological features are related to the two independent phases of the scattering matrix. A convenient scheme to generate topological edge states, and an effective Fabry-Perot cavity model are presented. Existing experimental realizations will be addressed, and results will be shown which extend beyond the dielectric Fibonacci sequence. |