On the Almost Reducibility Conjecture

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-02-05 DOI:10.1007/s00039-024-00671-0

引用次数: 0

Abstract

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.

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关于几乎可重复性猜想

摘要阿维拉的 "几乎可重复性猜想"（ARC）是将解析一频（SL(2,{\mathbb{R}})）环的纯解析性质和动力学性质联系起来的一个强有力的声明。它也是研究解析一频薛定谔算子谱理论的基本工具，具有许多惊人的后果，可以给出亚临界区的详细特征。在此，我们针对具有三角多项式势能和非指数近似频率的薛定谔环的重要情况，给出了与阿维拉完全不同的证明，特别是在这种情况下，我们可以得到所有想要的频谱结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464