A Kam Scheme for SL(2, \({{\mathbb R}}\)) Cocycles with Liouvillean Frequencies

  • Artur Avila
  • Bassam Fayad
  • Raphaël Krikorian


We develop a new KAM scheme that applies to SL(2, \({{\mathbb R}}\)) cocycles with one frequency, irrespective of any Diophantine condition on the base dynamics. It gives a generalization of Dinaburg–Sinai’s theorem to arbitrary frequencies: under a closeness to constant assumption, the non-Abelian part of the classical reducibility problem can always be solved for a positive measure set of parameters.

Keywords and phrases

Quasiperiodic cocycles ergodic Schrödinger operators reducibility 

2010 Mathematics Subject Classification

37J40 37E20 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.CNRS UMR 7586Institut de Mathématiques de JussieuParisFrance
  2. 2.CNRS UMR 7539, LAGAUniversité Paris 13VilletaneuseFrance
  3. 3.CNRS UMR 7599, Laboratoire de Probabilités et Modèles aléatoiresUniversité Pierre et Marie CurieParis Cedex 05France

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