Corpus ID: 119733273

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

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