Canonical structure of renormalization group equations and separability of Hamiltonian systems

Yoshiyuki Y. Yamaguchi; Yasusada Nambu

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arXiv · chao-dyn/9810010

Canonical structure of renormalization group equations and separability of Hamiltonian systems

Yoshiyuki Y. Yamaguchi·Yasusada Nambu

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Abstract

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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Yoshiyuki Y. Yamaguchi, Yasusada Nambu. 1998-10-07. Canonical structure of renormalization group equations and separability of Hamiltonian systems. https://arxiv.org/abs/chao-dyn/9810010

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