Joao Lopes-Dias
Renormalisation of flows on the multidimensional torus
(193K, PostScript)
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''.