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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/33826
On the computation of reducible invariant tori on a parallel computer
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We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around the torus and, hence, its linear stability. The algorithm presents a high degree of parallelism, and the computational effort grows linearly with the number of Fourier modes needed to represent the solution. For these reasons it is a very good option to compute quasi-periodic solutions with several basic frequencies. The paper includes some examples (flows) to show the efficiency of the method in a parallel computer. In these flows we compute invariant tori of dimensions up to 5, by taking suitable sections.
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JORBA I MONTE, Àngel and OLMEDO, Estrella. On the computation of reducible invariant tori on a parallel computer. SIAM Journal On Applied Dynamical Systems. 2009. Vol. 8, num. 4, pags. 1382-1404. ISSN 1536-0040. [consulted: 7 of October of 2026]. Available at: https://hdl.handle.net/2445/33826