On the almost reducibility conjecture

Lingrui Ge

On the almost reducibility conjecture

Dynamical Systems 2023-09-12 v2 Mathematical Physics math.MP Spectral Theory

Authors: Lingrui Ge

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.

Cite

@article{arxiv.2306.16376,
  title  = {On the almost reducibility conjecture},
  author = {Lingrui Ge},
  journal= {arXiv preprint arXiv:2306.16376},
  year   = {2023}
}

Comments

20 pages. arXiv admin note: text overlap with arXiv:1712.04700 by other authors

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