Robust computation of higher-dimensional invariant tori from individual trajectories
Abstract
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.
Keywords
Cite
@article{arxiv.2505.08715,
title = {Robust computation of higher-dimensional invariant tori from individual trajectories},
author = {Maximilian Ruth and Jackson Kulik and Joshua Burby},
journal= {arXiv preprint arXiv:2505.08715},
year = {2025}
}