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

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''.

final version

References in corpus (1)

• Renormalisation scheme for vector fields on T2 with a diophantine frequency

Cited by in corpus (4)

• Multidimensional continued fractions, dynamical renormalization and KAM theory
• Renormalisation scheme for vector fields on T2 with a diophantine frequency
• Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
• The Katok-Spatzier Conjecture and Generalized Symmetries