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A Renormalization Group for Hamiltonians: Numerical Results

Juan J. Abad·Hans Koch·Peter Wittwer
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Abstract

We describe a renormalization group transformation that is related to the breakup of golden invariant tori in Hamiltonian systems with two degrees of freedom. This transformation applies to a large class of Hamiltonians, is conceptually simple, and allows for accurate numerical computations. In a numerical implementation, we find a nontrivial fixed point and determine the corresponding critical index and scaling. Our computed values for various universal constants are in good agreement with existing data for area-preserving maps. We also discuss the flow associated with the nontrivial fixed point.

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BibTeXRIS

Juan J. Abad, Hans Koch, Peter Wittwer. 1998-04-17. A Renormalization Group for Hamiltonians: Numerical Results. https://doi.org/10.1088/0951-7715%2F11%2F5%2F001

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