Renormalization group equations and integrability in Hamiltonian systems
  We investigate Hamiltonian systems with two degrees of freedom by using renormalization group method. We show that the original Hamiltonian systems and the renormalization group equations are integrable if the renormalization group equations are Hamiltonian systems up to the second leading order of a small parameter. 
Yoshiyuki Y. Yamaguchi and Yasusada Nambu