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

By Artur Avila, Bassam Fayad, R. Krikorian. 2010

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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.

Subfields: Mathematical Physics, Spectroscopy, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5b12fd7f5d217bbe384496ae2ff17a82cdb67588