Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory

Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory

Year:    2022

Author:    Wenlei Li, Shaoyun Shi

Communications in Mathematical Research , Vol. 38 (2022), Iss. 1 : pp. 99–122

Abstract

In this paper, we mainly investigate three topics on the renormalization group (RG) method to singularly perturbed problems: 1) We will present an explicit strategy of RG procedure to get the approximate solution up to any order. 2) We will refer that the RG procedure can, in fact, be used to get the normal form of differential dynamical systems. 3) We will also present the approximating center manifolds of the perturbed systems, and investigate the long time asymptotic behavior by means of RG formula.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cmr.2021-0049

Communications in Mathematical Research , Vol. 38 (2022), Iss. 1 : pp. 99–122

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Renormalization group method normal form center manifolds.

Author Details

Wenlei Li

Shaoyun Shi

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