The spectral characteristics of the Sturm Hamiltonian with eventually periodic type

Abstract

In this paper we consider the spectral characteristics of the Sturm Hamiltonian with eventually periodic type frequencies under large coupling and establish strict inequalities between the optimal Hölder exponent of the density of states measure, the dimension of the density of states measure, the dimension of the spectrum, and the transport exponent by analyzing the thermodynamic pressure function. Also, we provide the large coupling asymptotic properties of the four spectral characteristics.

References in corpus (14)

• Lyapunov spectrum of asymptotically sub-additive potentials
• Schrödinger Operators with Dynamically Defined Potentials: A Survey
• Uniform spectral properties of one-dimensional quasicrystals, III. $\alpha$-continuity
• The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
• The Fibonacci Hamiltonian
• Spectral and Quantum Dynamical Properties of the Weakly Coupled Fibonacci Hamiltonian
• Bers and Hénon, Painlevé and Schroedinger
• Hyperbolicity of the Trace Map for the Weakly Coupled Fibonacci Hamiltonian
• Spectra of Discrete Schrödinger Operators with Primitive Invertible Substitution Potentials
• The fractal dimensions of the spectrum of Sturm Hamiltonian
• Dynamical Green Functions and Discrete Schrödinger Operators with Potentials Generated by Primitive Invertible Substitution
• Hölder Continuity of the Integrated Density of States for the Fibonacci 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