A parameterization method for quasi-periodic systems with noise: computation of random invariant tori
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910877787095040 |
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| author | Wei, Pingyuan Zhang, Lei |
| author_facet | Wei, Pingyuan Zhang, Lei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A parameterization method for quasi-periodic systems with noise: computation of random invariant tori Wei, Pingyuan Zhang, Lei Dynamical Systems 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. |
| title | A parameterization method for quasi-periodic systems with noise: computation of random invariant tori |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2503.12493 |