Hans Koch and Sasa Kocic
A renormalization group approach 
to quasiperiodic motion with Brjuno frequencies
(78K, plain TeX)

ABSTRACT.  We introduce a renormalization group scheme 
that applies to vector fields on $torus^d\times\real^m$ 
with frequency vectors that satisfy a Brjuno condition. 
Earlier approaches were restricted to Diophantine frequencies, 
due to a limited control of multidimensional continued fractions. 
We get around this restriction 
by avoiding the use of a continued fractions expansion. 
Our results concerning invariant tori generalize those of 
reference [17] from Diophantine to Brjuno type frequency vectors. 
In particular, each Brjuno vector $\omega\in\real^d$ determines 
an analytic manifold $W$ of infinitely renormalizable vector fields, 
and each vector field on $W$ is shown to have an elliptic 
invariant $d$-torus with frequencies $\omega_1,\omega_2,\ldots,\omega_d$.