The Spectral Properties of the Strongly Coupled Sturm Hamiltonian of Eventually Constant Type

摘要: We study the spectral properties of Sturm Hamiltolian eventually constant type, which includes Fibonacci Hamiltonian. Let s be Hausdorff dimension spectrum. For V > 20, we show that restriction s-dimensional measure to spectrum is a Gibbs type measure; density states Markov measure. Based on fine structures these measures, both measures are exact dimensional; obtain asymptotic behaviors for optimal Holder exponent and As consequence, if frequency not silver number then big enough, establish strict inequalities between three characteristics. achieve them by introducing an auxiliary symbolic dynamical system applying thermodynamical multifractal formalisms almost additive potentials.