Federico Bonetto, Giovanni Gallavotti, Guido Gentile,
Quasi linear flows on tori: regularity of their
linearization
(102K, tex)

ABSTRACT.  Under suitable conditions a flow on a torus
$C^{(p)}$--close, with $p$ large enough, to a quasi periodic
diophantine rotation is shown to be conjugated to the quasi
periodic rotation by a map that is analytic in the
perturbation size. This result is parallel to Moser's theorem
stating conjugability in class $C^{(p')}$ for some
$p'<p$. The extra conditions restrict the class of
perturbations that are allowed.