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Volume 38, Issue 1
Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory

Wenlei Li & Shaoyun Shi

DOI: 10.4208/cmr.2021-0049

Commun. Math. Res., 38 (2022), pp. 99-122.

Published online: 2021-11

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  • 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.

  • Keywords

Renormalization group method, normal form, center manifolds.

  • AMS Subject Headings

34D15, 34E05, 37D10, 37G05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-38-99, author = {Li , Wenlei and Shi , Shaoyun}, title = {Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {38}, number = {1}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0049}, url = {http://global-sci.org/intro/article_detail/cmr/19959.html} }
TY - JOUR T1 - Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory AU - Li , Wenlei AU - Shi , Shaoyun JO - Communications in Mathematical Research VL - 1 SP - 99 EP - 122 PY - 2021 DA - 2021/11 SN - 38 DO - http://doi.org/10.4208/cmr.2021-0049 UR - https://global-sci.org/intro/article_detail/cmr/19959.html KW - Renormalization group method, normal form, center manifolds. AB -

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.

Li , Wenlei and Shi , Shaoyun. (2021). Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory. Communications in Mathematical Research . 38 (1). 99-122. doi:10.4208/cmr.2021-0049
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