标题： 几乎局域化和几乎可约性 显示英文标题

标题： Almost localization and almost reducibility

摘要： 我们开发了一种Aubry对偶性的定量版本，并利用它来获得与非微扰小解析势和Diophantine频率相关的Schrödinger余弦的动态的一些精确估计。 特别是，在这种情况下，我们建立了Eliasson可约化理论的完整版本（我们的方法实际上在微扰范围内也带来了改进：我们能够证明，在某些解析性带中，所有能量都具有“几乎可约性”）。 我们还证明了积分态密度的1/2-Hölder连续性。 对于几乎数学家算子，我们的结果在整个亚临界耦合区域内成立，并且也意味着所涉及参数的Ten Martini问题的干燥版本。 显示英文摘要

摘要： We develop a quantitative version of Aubry duality and use it to obtain several sharp estimates for the dynamics of Schr\"odinger cocycles associated to a non-perturbatively small analytic potential and Diophantine frequency. In particular, we establish the full version of Eliasson's reducibility theory in this regime (our approach actually leads to improvements even in the perturbative regime: we are able to show, for all energies, ``almost reducibility'' in some band of analyticity). We also prove 1/2-H\"older continuity of the integrated density of states. For the almost Mathieu operator, our results hold through the entire regime of sub-critical coupling and imply also the dry version of the Ten Martini Problem for the concerned parameters.