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

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

2001-05-09

arxiv.org/abs/math/0105066v2

Mathematics

Dynamical Systems

final version

Scientific paper

10.1088/0951-7715/15/3/307

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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