A parameterization method for quasi-periodic systems with noise: computation of random invariant tori
Dynamical Systems
2025-03-18 v1
Abstract
This work is devoted to studying normally hyperbolic invariant manifolds (NHIMs) for a class of quasi-periodically forced systems subject to additional stochastic noise. These systems can be understood as skew-product systems. The existence of NHIMs is established by developing a parameterization method in random settings and applying the Implicit Function Theorem in appropriate Banach spaces. Based on this, we propose a numerical algorithm to compute the statistics of NHIMs and Lyapunov exponents.
Keywords
Cite
@article{arxiv.2503.12493,
title = {A parameterization method for quasi-periodic systems with noise: computation of random invariant tori},
author = {Pingyuan Wei and Lei Zhang},
journal= {arXiv preprint arXiv:2503.12493},
year = {2025}
}