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arXiv · 2503.12493

A parameterization method for quasi-periodic systems with noise: computation of random invariant tori

Pingyuan Wei·Lei Zhang
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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.

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Pingyuan Wei, Lei Zhang. 2025-03-16. A parameterization method for quasi-periodic systems with noise: computation of random invariant tori. https://arxiv.org/abs/2503.12493

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