Dynamical Green Functions and Discrete Schrödinger Operators with Potentials Generated by Primitive Invertible Substitution

Arnaud Girand (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we set up a "dictionary" between discrete Schrödinger operators and the holomorphic dynamics on certain affine cubic surfaces, building on previous work by Cantat, Damanik and Gorodetski. Paragraphs 3.2.2 and 3.2.3 were written by Serge Cantat as an appendix.

Mots clés: Dynamical Green Functions; Discrete Schrödinger Operators; Holomorphic Dynamics

Domaines: Systèmes dynamiques [math.DS]

Arnaud Girand. Dynamical Green Functions and Discrete Schrödinger Operators with Potentials Generated by Primitive Invertible Substitution. Nonlinearity, 2014, 27 (3), pp.527-543. ⟨10.1088/0951-7715/27/3/527⟩. ⟨hal-00864671v2⟩