Canonical structure of renormalization group equations and separability of Hamiltonian systems

Details Canonical structure of renormalization group equations and separability of Hamiltonian systems Canonical structure of renormalization group equations and separability of Hamiltonian systems

1998-10-07

arxiv.org/abs/chao-dyn/9810010v1

Nonlinear Sciences

Chaotic Dynamics

21 pages, LaTeX (58 kb)

Scientific paper

We investigate perturbed Hamiltonian systems with two degrees of freedom by renormalization group method, which derives a reduced equation called renormalization group equation (RGE) by handling secular terms. We found that RGE is not always a Hamiltonian system. The necessary and sufficient condition that RGE becomes a Hamiltonian system up to the second leading order of a small parameter is that the original system is separable by Cartesian coordinates. Moreover, RGE is integrable when it is a Hamiltonian system. These statements are partial generalizations of our previous paper.

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