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首页> 外文期刊>Annales Henri Poincare >The Spectral Properties of the Strongly Coupled Sturm Hamiltonian of Eventually Constant Type
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The Spectral Properties of the Strongly Coupled Sturm Hamiltonian of Eventually Constant Type

机译：最终定型的强耦合Sturm哈密顿量的谱性质

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摘要

We study the spectral properties of the Sturm Hamiltolian of eventually constant type, which includes the Fibonacci Hamiltonian. Let s be the Hausdorff dimension of the spectrum. For V > 20, we show that the restriction of the s-dimensional Hausdorff measure to the spectrum is a Gibbs type measure; the density of states measure is a Markov measure. Based on the fine structures of these measures, we show that both measures are exact dimensional; we obtain exact asymptotic behaviors for the optimal Holder exponent and the Hausdorff dimension of the density of states measure and for the Hausdorff dimension of the spectrum. As a consequence, if the frequency is not silver number type, then for V big enough, we establish strict inequalities between these three spectral characteristics. We achieve them by introducing an auxiliary symbolic dynamical system and applying the thermodynamical and multifractal formalisms of almost additive potentials.
机译：我们研究了最终恒定类型的Sturm Hamiltolian的光谱特性，其中包括Fibonacci Hamiltonian。让我们为频谱的Hausdorff维数。对于V> 20，我们证明s维Hausdorff测度对频谱的限制是Gibbs型测度;状态密度度量是马尔可夫度量。基于这些度量的精细结构，我们表明这两个度量都是精确的尺寸;我们获得了最佳Holder指数和状态密度的Hausdorff维数以及频谱的Hausdorff维数的精确渐近行为。结果，如果频率不是银数类型，那么对于足够大的V，我们在这三个频谱特性之间建立严格的不等式。我们通过引入辅助符号动力学系统并应用几乎具有加和势的热力学和多重分形形式来实现它们。

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