Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory (Communications in Mathematical Research, 2021)
In this paper, we mainly investigate three topics on the renormalization group (RG) method to singularly perturbed problems: 1) We will presentan explicit strategy of RG procedure to get the approximate solution up to anyorder. 2) We will refer that the RG procedure can, in fact, be used to get thenormal form of differential dynamical systems. 3) We will also present theapproximating center manifolds of the perturbed systems, and investigate thelong time asymptotic behavior by means of RG formula.