The spectral characteristics of the Sturm Hamiltonian with eventually periodic type

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.