Dynamical Green functions and discrete Schrödinger operators with potentials generated by primitive invertible substitution

In this paper, we set up a 'dictionary' between discrete Schrödinger operators and holomorphic dynamics on certain affine cubic surfaces, building on previous work by Cantat, Damanik and Gorodetski. To achieve this, we make use of potential theory: a detailed description of the dynamical Green functions is obtained; then basic results concerning the equilibrium measures and the Green functions of compact subsets of C are used to transfer statements from the dynamical context to the Schrödinger one. This provides a new viewpoint on several recent theorems. (paper)