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Renormalisation of flows on the multidimensional torus close to a KT frequency vector

Joao Lopes-Dias
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Abstract

We use a renormalisation operator R acting on a space of vector fields on the d-torus, d>1, to prove the existence of a submanifold of vector fields equivalent to constant. The result comes from the existence of a fixed point w of R which is hyperbolic. This is done for a certain class KT of constant vector fields w, called of Koch type. The transformation R is constructed using a time rescaling, a linear change of basis plus a periodic non-linear map isotopic to the identity, which we derive by a ``homotopy trick''.

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Joao Lopes-Dias. 2002-02-13. Renormalisation of flows on the multidimensional torus close to a KT frequency vector. https://doi.org/10.1088/0951-7715%2F15%2F3%2F307

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