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 H\"older exponent and As consequence, if frequency not silver number then $V$ big enough, establish strict inequalities between three characteristics. We achieve them by introducing an auxiliary symbolic dynamical system applying thermodynamical multifractal formalisms almost additive potentials.