01-191 Hans Koch

On the Renormalization of Hamiltonian Flows, and Critical Invariant Tori (54K, plain TeX) May 25, 01

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Abstract. We analyze a renormalization group transformation R for partially analytic Hamiltonians, with emphasis on what seems to be needed for the construction of non-integrable fixed points. Under certain assumptions, which are supported by numerical data in the golden mean case, we prove that such a fixed point has a critical invariant torus. The proof is constructive and can be used for numerical computations. We also relate R to a renormalization group transformation for commuting maps.

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