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Renormalisation scheme for vector fields on T2 with a diophantine frequency

Joao Lopes-Dias
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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.

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Joao Lopes-Dias. 2002-02-13. Renormalisation scheme for vector fields on T2 with a diophantine frequency. https://doi.org/10.1088/0951-7715%2F15%2F3%2F308

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