pith. sign in

arxiv: 1006.0704 · v1 · submitted 2010-06-03 · 🧮 math.DS

Almost reducibility and absolute continuity I

Artur Avila This is my paper
classification 🧮 math.DS
keywords almostcocyclesone-frequencyreducibilityworkabsoluteabsolutelyanalysis
0
0 comments X
read the original abstract

We consider one-frequency analytic SL(2,R) cocycles. Our main result establishes the Almost Reducibility Conjecture in the case of exponentially Liouville frequencies. Together with our earlier work, this implies that all cocycles close to constant are almost reducible, independent of the frequency. In our forthcoming work, we discuss applications to the analysis of the absolutely continuous spectrum of one-frequency Schrodinger operators.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Monotonicity, global symplectification and the stability of Dry Ten Martini Problem

    math.DS 2026-01 unverdicted novelty 8.0

    Type I energies with positive Lyapunov exponent and gap-labelling condition bound open spectral gaps for irrational frequencies and trig-polynomial potentials, making the all-gaps-open property robust for perturbed al...