On the almost reducibility conjecture

Lingrui Ge

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arXiv · 2306.16376

On the almost reducibility conjecture

Lingrui Ge

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Abstract

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

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BibTeX RIS

Lingrui Ge. 2023-06-28. On the almost reducibility conjecture. https://arxiv.org/abs/2306.16376

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