 99201 C. Chandre, H.R. Jauslin
 Strange attractor for the renormalization flow for invariant tori of Hamiltonian systems with two generic frequencies
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May 31, 99

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Abstract. We analyze the stability of invariant tori for Hamiltonian systems
with two degrees of freedom by constructing a transformation that
combines KolmogorovArnoldMoser theory and renormalizationgroup techniques.
This transformation is based on the continued fraction expansion
of the frequency of the torus.
We apply this transformation numerically for arbitrary frequencies
that contain bounded entries in the continued fraction expansion.
We give a global picture of renormalization flow for the stability of
invariant tori, and we show that the properties of critical (and near critical) tori can be obtained by analyzing renormalization dynamics around a single hyperbolic strange attractor. We compute the fractal diagram, i.e., the critical coupling as a function of the frequencies,
associated with a given oneparameter family.
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