A note on cocycles in $\mathbb{T}\times SO(3)$
Abstract
This short note studies $C^{\infty}$-smooth cocycles in $\mathbb{T}\times SO(3)$ that have $0$ degree and are non-homotopic to constants. The study picks up from where the author's PhD thesis left the subject, and shows that, under a relevant and full measure arithmetic condition, such cocycles can be conjugated to a simple model. Moreover, under the same arithmetic condition, the cocycle can be conjugated arbitrarily close to constant cocycles by a $2$-periodic conjugation.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
Geometric and Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 February 2026
- Language
- EN
- Document type
- Preprint