Avila’s Almost Reducibility Conjecture (ARC) is a powerful statement linking purely analytic and dynamical properties of analytic one-frequency \(SL(2,{\mathbb{R}})\) cocycles. It is also a fundamental tool in the study of spectral theory of analytic one-frequency Schrödinger operators, with many striking consequences, allowing to give a detailed characterization of the subcritical region. Here we give a proof, completely different from Avila’s, for the important case of Schrödinger cocycles with trigonometric polynomial potentials and non-exponentially approximated frequencies, allowing, in particular, to obtain all the desired spectral consequences in this case.

阿维拉的几乎可约化猜想 (ARC) 是一个强有力的陈述，它将解析单频\(SL(2,{\mathbb{R}})\)余循环的纯解析性质和动力学性质联系起来。它也是解析单频薛定谔算子谱理论研究的基本工具，具有许多引人注目的结果，可以对亚临界区域进行详细表征。在这里，我们针对具有三角多项式势和非指数近似频率的薛定谔余循环的重要情况给出了与阿维拉完全不同的证明，特别是允许在这种情况下获得所有所需的谱结果。