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arXiv · 1903.01914

Fibered rotation vector and hypoellipticity for quasiperiodic cocycles in compact Lie groups

Nikolaos Karaliolios
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Abstract

Using weak solutions to the conjugation equation, we define a fibered rotation vector for almost reducible quasi-periodic cocycles in $\mathbb{T}^{d} \times G$, $G$ a compact Lie group, over a Diophantine rotation. We then prove that if this rotation vector is Diophantine with respect to the rotation in $\mathbb{T}^{d}$, the cocycle is smoothly reducible, thus establishing a hypoellipticity property in the spirit of the Greenfield-Wallach conjecture in PDEs.

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Nikolaos Karaliolios. 2019-03-05. Fibered rotation vector and hypoellipticity for quasiperiodic cocycles in compact Lie groups. https://doi.org/10.1112/blms.12321

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