Renormalisation scheme for vector fields on T2 with a diophantine frequency

Joao Lopes-Dias

Published 2001-05-09, updated 2002-02-13Version 2

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