 06269 Hans Koch and Sasa Kocic
 A renormalization group approach
to quasiperiodic motion with Brjuno frequencies
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Sep 27, 06

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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 $\omega_1,\omega_2,\ldots,\omega_d$.
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