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Article Dans Une Revue Bulletin de la société mathématique de France Année : 2013

Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles

Claire Chavaudret
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Résumé

This paper is about almost reducibility of quasi-periodic cocycles with a diophantine frequency which are sufficiently close to a constant. Generalizing previous works by L.H.Eliasson, we show a strong version of almost reducibility for analytic and Gevrey cocycles, that is to say, almost reducibility where the change of variables is in an analytic or Gevrey class which is independent of how close to a constant the initial cocycle is conjugated. This implies a result of density, or quasi-density, of reducible cocycles near a constant. Some algebraic structure can also be preserved, by doubling the period if needed.
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Dates et versions

hal-00442730 , version 1 (22-12-2009)
hal-00442730 , version 2 (06-01-2010)
hal-00442730 , version 3 (04-06-2010)

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Claire Chavaudret. Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles. Bulletin de la société mathématique de France, 2013, 141 (1), pp.47-106. ⟨hal-00442730v3⟩
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