American Institue of Mathematical Sciences

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

On the renormalization of Hamiltonian flows, and critical invariant tori

 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.
Citation: Hans Koch. On the renormalization of Hamiltonian flows, and critical invariant tori. Discrete & Continuous Dynamical Systems - A, 2002, 8 (3) : 633-646. doi: 10.3934/dcds.2002.8.633
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