Numerical Computation of Quasiperiodic Reducible Saddle-Node Bifurcations: a Parameterization Method Approach
Dynamical Systems
2026-07-03 v1 Chaotic Dynamics
Abstract
We present a method for computing reducible, normally hyperbolic, invariant tori with internal quasiperiodic dynamics in autonomous ordinary differential equation systems. The approach is based on the parameterization method of KAM theory; thus, it is a Newton scheme with small divisors. Since the inner dynamics of the torus is prescribed, the corresponding system parameters for which such a torus exists are simultaneously determined. The method is amenable to a form of pseudo-arclength continuation, enabling the traversal and computation of saddle-node bifurcations. We give explicit algorithms for the methods and demonstrate their applicability with two numerical examples.
Cite
@article{arxiv.2607.03498,
title = {Numerical Computation of Quasiperiodic Reducible Saddle-Node Bifurcations: a Parameterization Method Approach},
author = {Jordi-Lluís Figueras and Joan Gimeno and Jeremy P. Parker},
journal= {arXiv preprint arXiv:2607.03498},
year = {2026}
}