Non-resonant invariant foliations of quasi-periodically forced systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913277060055040 |
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| author | Szalai, Robert |
| author_facet | Szalai, Robert |
| contents | We show the existence and uniqueness of invariant foliations about invariant tori in analytic discrete-time dynamical systems. The parametrisation method is used prove the result. Our theory is a foundational block of data-driven model order reduction, that can only be carried out using invariant foliations. The theory is illustrated by two mechanical examples, where instantaneous frequencies and damping ratios are calculated about the invariant tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14771 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-resonant invariant foliations of quasi-periodically forced systems Szalai, Robert Dynamical Systems We show the existence and uniqueness of invariant foliations about invariant tori in analytic discrete-time dynamical systems. The parametrisation method is used prove the result. Our theory is a foundational block of data-driven model order reduction, that can only be carried out using invariant foliations. The theory is illustrated by two mechanical examples, where instantaneous frequencies and damping ratios are calculated about the invariant tori. |
| title | Non-resonant invariant foliations of quasi-periodically forced systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2403.14771 |