01-172 Joao Lopes-Dias

Renormalisation of flows on the multidimensional torus (193K, PostScript) May 9, 01

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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 of constant vector fields w. 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''.

Files: 01-172.src( 01-172.keywords , renorm1.ps.gz.mm )