The spectral characteristics of the Sturm Hamiltonian with eventually periodic type

TL;DR

This paper analyzes the spectral properties of the Sturm Hamiltonian with eventually periodic frequencies, establishing inequalities among key spectral measures and exploring their asymptotic behavior at large coupling.

Contribution

It provides new inequalities and asymptotic results for spectral characteristics of Sturm Hamiltonians with eventually periodic frequencies.

Findings

Established inequalities between spectral measures and dimensions.

Analyzed the thermodynamic pressure function.

Derived large coupling asymptotic properties.

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 H\"older 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.