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DC Field | Value | Language |
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dc.contributor.author | Gimeno, Joan | - |
dc.contributor.author | Jorba i Monte, Àngel | - |
dc.contributor.author | Nicolás, Begoña | - |
dc.contributor.author | Olmedo, Estrella | - |
dc.date.accessioned | 2023-03-02T11:05:38Z | - |
dc.date.available | 2023-03-02T11:05:38Z | - |
dc.date.issued | 2022-09 | - |
dc.identifier.issn | 1536-0040 | - |
dc.identifier.uri | http://hdl.handle.net/2445/194435 | - |
dc.description.abstract | In this paper we present a procedure to compute reducible invariant tori and their stable and unstable manifolds in Poincaré maps. The method has two steps. In the first step we compute, by means of a quadratically convergent scheme, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. If the torus has stable and/or unstable directions, in the second step we compute the Taylor--Fourier expansions of the corresponding invariant manifolds up to a given order. The paper also discusses the case in which the torus is highly unstable so that a multiple shooting strategy is needed to compute the torus. If the order of the Taylor expansion of the manifolds is fixed and $N$ is the number of Fourier modes, the whole computational effort (torus and manifolds) increases as $\mathcal{O}(N \log N)$ and the memory required behaves as $\mathcal{O}(N)$. This makes the algorithm very suitable to compute highdimensional tori for which a huge number of Fourier modes are needed. Besides, the algorithm has a very high degree of parallelism. The paper includes examples where we compute invariant tori (of dimensions up to 5) of quasiperiodically forced ODEs. The computations are run in a parallel computer, and the method's efficiency with respect to the number of processors is also discussed. | - |
dc.format.extent | 30 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Society for Industrial and Applied Mathematics. | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.1137/21M1458363 | - |
dc.relation.ispartof | SIAM Journal On Applied Dynamical Systems, 2022, vol. 21, num. 3, p. 1832-1861 | - |
dc.relation.uri | https://doi.org/10.1137/21M1458363 | - |
dc.rights | (c) Society for Industrial and Applied Mathematics., 2022 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Sistemes dinàmics diferenciables | - |
dc.subject.classification | Anàlisi numèrica | - |
dc.subject.classification | Processament en paral·lel (Ordinadors) | - |
dc.subject.other | Differentiable dynamical systems | - |
dc.subject.other | Numerical analysis | - |
dc.subject.other | Parallel processing (Electronic computers) | - |
dc.title | Numerical computation of high-order expansions of invariant manifolds of high-dimensional tori | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 731059 | - |
dc.date.updated | 2023-03-02T11:05:38Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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File | Description | Size | Format | |
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731059.pdf | 416.25 kB | Adobe PDF | View/Open |
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