Kernel methods for center manifold approximation and a weak data-based version of the Center Manifold Theorem

For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means center manifold theory. This theory allows isolate complicated asymptotic behavior system close equilibrium point and obtain meaningful predictions its analyzing reduced order on so-called manifold. Since usually not known, good approximation methods are important as theorem states that properties origin same those full system. In this work, we establish data-based version works considering an in place exact Also error between approximated original dynamics quantified. We then use apposite kernel method construct suitable which compatible our general The data collected repeated numerical simulation high-accuracy solver, generates sets discrete trajectories used training set. tested different examples show promising performance accuracy. • prove weak Center Manifold Theorem using how build sampling trajectories. derive provably accurate algorithm for task.