On the renormalization of Hamiltonian flows, and critical invariant tori (Q1599883)
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scientific article; zbMATH DE number 1751467
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the renormalization of Hamiltonian flows, and critical invariant tori |
scientific article; zbMATH DE number 1751467 |
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On the renormalization of Hamiltonian flows, and critical invariant tori (English)
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6 June 2002
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We analyze a renormalization group transformation \(\mathcal R\) 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 \(\mathcal R\) to a renormalization group transformation for commuting maps.
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