Renormalisation scheme for vector fields on T2 with a diophantine frequency

Abstract

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.

final version

References in corpus (2)

• Renormalisation of flows on the multidimensional torus close to a KT frequency vector
• Scaling law for the critical function of an approximate renormalization

Cited by in corpus (2)

• Multidimensional continued fractions, dynamical renormalization and KAM theory
• Renormalisation of flows on the multidimensional torus close to a KT frequency vector