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Differentiable Rigidity for quasiperiodic cocycles in compact Lie groups

  • Author Bio: Nikolaos Karaliolios nikolaos.karaliolios@imj-prg.fr
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  • We study close-to-constants quasiperiodic cocycles in $\mathbb{T} ^{d} \times G$ , where $d \in \mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the assumption that the rotation in the basis satisfies a Diophantine condition. We prove differentiable rigidity for such cocycles: if such a cocycle is measurably conjugate to a constant one satisfying a Diophantine condition with respect to the rotation, then it is $C^{\infty}$ -conjugate to it, and the KAM scheme actually produces a conjugation. We also derive a global differentiable rigidity theorem, assuming the convergence of the renormalization scheme for such dynamical systems.

    Mathematics Subject Classification: Primary: 37C55.


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