2025/05/13 by Ruth, Maximilian, Kulik, Jackson, Burby, Joshua · 2 citations
#Computational Physics (physics.comp-ph) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences
paper · doi:10.48550/arxiv.2505.08715
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 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.