- 05-285 Hans Koch and Joao Lopes Dias
- Renormalization of Diophantine Skew Flows,
with Applications to the Reducibility Problem
(99K, plain TeX)
Aug 23, 05
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Abstract. We introduce a renormalization group framework
for the study of quasiperiodic skew flows on Lie groups
of real or complex n x n matrices, for arbitrary
diophantine frequency vectors in R^d and dimensions d,n.
In cases where the group component of the vector field is small,
it is shown that there exists an analytic manifold
of reducible skew systems, for each diophantine frequency vector.
More general near-linear flows are mapped to this case
by increasing the dimension of the torus.
This strategy is applied for the group of unimodular
2 x 2 matrices, where the stable manifold is identified
with the set of skew systems having a fixed fibered rotation number.
Our results apply to vector fields of class C^r,
with r depending on the number of independent frequencies,
and on the diophantine exponent.