Mathematics – Dynamical Systems
Scientific paper
2001-05-09
Mathematics
Dynamical Systems
final version
Scientific paper
10.1088/0951-7715/15/3/308
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.
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