Robust computation of higher-dimensional invariant tori from individual trajectories
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_ | 1866912373855485952 |
|---|---|
| author | Ruth, Maximilian Kulik, Jackson Burby, Joshua |
| author_facet | Ruth, Maximilian Kulik, Jackson Burby, Joshua |
| contents | We present a method for computing invariant tori of dimension greater than one. The method uses a single short trajectory of a dynamical system without any continuation or initial guesses. No preferred coordinate system is required, meaning the method is practical for physical systems where the user does not have much \textit{a priori} knowledge. Three main tools are used to obtain the rotation vector of the invariant torus: the reduced rank extrapolation method, Bayesian maximum a posteriori estimation, and a Korkine-Zolatarev lattice basis reduction. The parameterization of the torus is found via a least-squares approach. The robustness of the algorithm is demonstrated by accurately computing many two-dimensional invariant tori of a standard map example. Examples of islands and three-dimensional invariant tori are shown as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08715 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust computation of higher-dimensional invariant tori from individual trajectories Ruth, Maximilian Kulik, Jackson Burby, Joshua Dynamical Systems Computational Physics We present a method for computing invariant tori of dimension greater than one. The method uses a single short trajectory of a dynamical system without any continuation or initial guesses. No preferred coordinate system is required, meaning the method is practical for physical systems where the user does not have much \textit{a priori} knowledge. Three main tools are used to obtain the rotation vector of the invariant torus: the reduced rank extrapolation method, Bayesian maximum a posteriori estimation, and a Korkine-Zolatarev lattice basis reduction. The parameterization of the torus is found via a least-squares approach. The robustness of the algorithm is demonstrated by accurately computing many two-dimensional invariant tori of a standard map example. Examples of islands and three-dimensional invariant tori are shown as well. |
| title | Robust computation of higher-dimensional invariant tori from individual trajectories |
| topic | Dynamical Systems Computational Physics |
| url | https://arxiv.org/abs/2505.08715 |