  Topological insulators and superconductors are characterized by their gapless
boundary modes. In this paper, we develop a recursive approach to the boundary
Green function which encodes this nontrivial boundary physics. Our approach
describes the various topologically trivial and nontrivial phases as fixed
points of a recursion and provides direct access to the phase diagram, the
localization properties of the edge modes, as well as topological indices. We
illustrate our approach in the context of various familiar models such as the
Su-Schrieffer-Heeger model, the Kitaev chain, and a model for a Chern
insulator. We also show that the method provides an intuitive approach to
understand recently introduced topological phases which exhibit gapless corner
states.
