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

Abstract

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.

18 pages

Cited by in corpus (7)

• Schrödinger Operators with Dynamically Defined Potentials: A Survey
• The Fibonacci Hamiltonian
• Spectra of Discrete Schrödinger Operators with Primitive Invertible Substitution Potentials
• On the Hausdorff dimension of the spectrum of Thue-Morse Hamiltonian
• The spectral properties of the strongly coupled Sturm Hamiltonian of eventually constant type
• Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians
• The spectral characteristics of the Sturm Hamiltonian with eventually periodic type