标题： 干十Martini问题对于Sturmian哈密顿量 显示英文标题

标题： The Dry Ten Martini Problem for Sturmian Hamiltonians

摘要： 干十马丁问题对于斯托尔姆哈密顿量被肯定解决。 具体来说，我们证明了对于非零耦合常数的斯托尔姆势的薛定谔算子，所有谱间隙都是开放的。 解决问题的一个关键方法是将谱表示为无限树的边界。 这棵树通过特定的周期逼近构造，并编码了重要的谱特性。 显示英文摘要

摘要： The Dry Ten Martini Problem for Sturmian Hamiltonians is affirmatively solved. Concretely, we prove that all spectral gaps are open for Schr\"odinger operators with Sturmian potentials and non-vanishing coupling constant. A key approach towards the solution is a representation of the spectrum as the boundary of an infinite tree. This tree is constructed via particular periodic approximations and it encodes substantial spectral characteristics.