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We construct a rigorous renormalisation scheme for analytic vector fields onthe 2-torus of Poincare type. We show that iterating this procedure there isconvergence to a limit set with a ``Gauss map'' dynamics on it, related to thecontinued fraction expansion of the slope of the frequencies. This is valid fordiophantine frequency vectors.Comment: final versio

Renormalization scheme for vector fields on 𝕋2with a diophantine frequency

Renormalization scheme for vector fields on 𝕋²with a diophantine frequency