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July  2002, 8(3): 633-646. doi: 10.3934/dcds.2002.8.633

On the renormalization of Hamiltonian flows, and critical invariant tori

Hans Koch 1,

1. 

Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, United States

Received  August 2001 Revised  November 2001 Published  April 2002

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.
Keywords: fixed point., Hamiltonian flows.
Mathematics Subject Classification: 58F22, 58F2.
Citation: Hans Koch. On the renormalization of Hamiltonian flows, and critical invariant tori. Discrete & Continuous Dynamical Systems, 2002, 8 (3) : 633-646. doi: 10.3934/dcds.2002.8.633
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