Renormalisation of flows on the multidimensional torus
نویسنده
چکیده
We use a renormalisation operator R acting on a space of vector fields on T, d ≥ 2, to prove the existence of a submanifold of vector fields equivalent to constant. The result comes from the existence of a fixed point ω of R which is hyperbolic. This is done for a certain class of constant vector fields ω. 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”.
منابع مشابه
Renormalisation of flows on the multidimensional torus close to a KT frequency vector
We use a renormalisation operator R acting on a space of vector fields on T, d ≥ 2, to prove the existence of a submanifold of vector fields equivalent to constant. The result comes from the existence of a fixed point ω of R which is hyperbolic. This is done for a certain class KTd of frequency vectors ω ∈ R, called of Koch type. The transformation R is constructed using a time rescaling, a lin...
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