Local conjugacy classes for analytic torus flows

Mathematics – Dynamical Systems

Scientific paper

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Scientific paper

If a real-analytic flow on the multidimensional torus close enough to linear
has a unique rotation vector which satisfies an arithmetical condition Y, then
it is analytically conjugate to linear. We show this by proving that the orbit
under renormalization of a constant Y vector field attracts all nearby orbits
with the same rotation vector.

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