Renormalisation scheme for vector fields on T2 with a diophantine frequency
Dynamical Systems
2009-11-07 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.math/0105067,
title = {Renormalisation scheme for vector fields on T2 with a diophantine frequency},
author = {Joao Lopes-Dias},
journal= {arXiv preprint arXiv:math/0105067},
year = {2009}
}
Comments
final version