# Invariant Distributions and local theory of quasiperiodic cocycles in $\mathbb{T} ^{d} \times SU(2)$}

@article{Karaliolios2014InvariantDA, title={Invariant Distributions and local theory of quasiperiodic cocycles in \$\mathbb\{T\} ^\{d\} \times SU(2)\$\}}, author={Nikolaos Karaliolios}, journal={arXiv: Dynamical Systems}, year={2014} }

We study the linear cohomological equation in the smooth category over quasi-periodic cocycles in $\mathbb{T} ^{d} \times SU(2)$. We prove that, under a full measure condition on the rotation in $\mathbb{T} ^{d}$, for a generic cocycle in an open set of cocycles, the equation admits a solution for a dense set of functions on $\mathbb{T} ^{d} \times SU(2)$ of zero average with respect to the Haar measure. This property is known as Distributional Unique Ergodicity (DUE). We then show that given… Expand

#### 2 Citations

Continuous Spectrum or Measurable Reducibility for Quasiperiodic Cocycles in $${\mathbb{T} ^{d} \times SU(2)}$$Td×SU(2)

- Physics, Mathematics
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AbstractWe continue our study of the local theory for quasiperiodic cocycles in $${\mathbb{T} ^{d} \times G}$$Td×G , where $${G=SU(2)}$$G=SU(2) , over a rotation satisfying a Diophantine condition… Expand

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

- Mathematics
- Bulletin of the London Mathematical Society
- 2020

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… Expand

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