Renormalization group based implicit function approach to connecting orbits
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913921344995328 |
|---|---|
| author | Guo, Pengfei Lan, Yueheng Qiao, Jianyong |
| author_facet | Guo, Pengfei Lan, Yueheng Qiao, Jianyong |
| contents | Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on renormalization group, an implicit function scheme is designed to effectively represent connections of disparate types, where coefficients of the defining function satisfy a set of linear algebraic equations, which greatly simplifies their computation. Unknown system parameters are conveniently determined by minimizing an error function. Symmetry may be profitably utilized to reduce the computation load. Homoclinic or heteroclinic connections are found in five popular examples approximately or exactly, demonstrating the effectiveness of the new scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Renormalization group based implicit function approach to connecting orbits Guo, Pengfei Lan, Yueheng Qiao, Jianyong Mathematical Physics Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on renormalization group, an implicit function scheme is designed to effectively represent connections of disparate types, where coefficients of the defining function satisfy a set of linear algebraic equations, which greatly simplifies their computation. Unknown system parameters are conveniently determined by minimizing an error function. Symmetry may be profitably utilized to reduce the computation load. Homoclinic or heteroclinic connections are found in five popular examples approximately or exactly, demonstrating the effectiveness of the new scheme. |
| title | Renormalization group based implicit function approach to connecting orbits |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2507.00749 |