Fibered rotation vector and hypoellipticity for quasi‐periodic cocycles in compact Lie groups

Abstract

Using weak solutions to the conjugation equation, we define a fibered rotation vector for almost reducible quasi‐periodic cocycles in double-struckTd×G, G a compact Lie group, over a Diophantine rotation. We then prove that if this rotation vector is Diophantine with respect to the rotation in Td, the cocycle is smoothly reducible, thus establishing a hypoellipticity property in the spirit of the Greenfield–Wallach conjecture in PDEs.

Erratum

“…Between September 2019 and February 2020, twenty‐one research articles 1–21 were published in the Bulletin of the London Mathematical Society with incorrect copyright statements. The copyright in these articles is stated as belonging to the London Mathematical Society; however, that is incorrect and the copyright remains with the authors of those articles.…”