Canonical structure of renormalization group equations and separability of Hamiltonian systems

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.

21 pages, LaTeX (58 kb)

References in corpus (3)

• Long-Time Correlations in the Stochastic Regime
• Renormalization group equations and integrability in Hamiltonian systems
• A Geometrical Model for Stagnant Motion in Hamiltonian Systems with Many Degrees of Freedom