Functional relations in renormalization group methods for a class of ordinary differential equations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915909058166784 |
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| author | Kuniba, Atsuo Motohashi, Rurika |
| author_facet | Kuniba, Atsuo Motohashi, Rurika |
| contents | We develop a renormalization group (RG)-based perturbation scheme for a class of ordinary differential equations, including first-order systems with semisimple or nilpotent linear parts, as well as scalar higher-order equations. The key observation is that the secular coefficients arising in naive perturbation theory satisfy an exact functional relation. This yields, in a unified manner, several fundamental features of the RG method: the renormalized amplitudes satisfy a closed functional relation with a group-like structure, the RG equation governing their slow dynamics is obtained directly, the absence of secular terms is ensured to all orders, and the relation between bare and renormalized amplitudes admits an explicit inversion. The results extend earlier ones for second-order scalar equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01744 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Functional relations in renormalization group methods for a class of ordinary differential equations Kuniba, Atsuo Motohashi, Rurika Mathematical Physics Dynamical Systems 34C20 (Primary), 34E10 (Secondary) We develop a renormalization group (RG)-based perturbation scheme for a class of ordinary differential equations, including first-order systems with semisimple or nilpotent linear parts, as well as scalar higher-order equations. The key observation is that the secular coefficients arising in naive perturbation theory satisfy an exact functional relation. This yields, in a unified manner, several fundamental features of the RG method: the renormalized amplitudes satisfy a closed functional relation with a group-like structure, the RG equation governing their slow dynamics is obtained directly, the absence of secular terms is ensured to all orders, and the relation between bare and renormalized amplitudes admits an explicit inversion. The results extend earlier ones for second-order scalar equations. |
| title | Functional relations in renormalization group methods for a class of ordinary differential equations |
| topic | Mathematical Physics Dynamical Systems 34C20 (Primary), 34E10 (Secondary) |
| url | https://arxiv.org/abs/2604.01744 |