Kolmogorov variation: KAM with knobs (à la Kolmogorov)
In this paper we reconsider the original Kolmogorov normal form algorithm [26] with a variation on the handling of the frequencies. At difference with respect to the Kolmogorov approach, we do not keep the frequencies fixed along the normalization procedure. Besides, we select the frequencies of the...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-10-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023089?viewType=HTML |
| _version_ | 1797448849906728960 |
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| author | Marco Sansottera Veronica Danesi |
| author_facet | Marco Sansottera Veronica Danesi |
| author_sort | Marco Sansottera |
| collection | DOAJ |
| description | In this paper we reconsider the original Kolmogorov normal form algorithm [26] with a variation on the handling of the frequencies. At difference with respect to the Kolmogorov approach, we do not keep the frequencies fixed along the normalization procedure. Besides, we select the frequencies of the final invariant torus and determine a posteriori the corresponding starting ones. In particular, we replace the classical translation step with a change of the frequencies. The algorithm is based on the original scheme of Kolmogorov, thus exploiting the fast convergence of the Newton-Kantorovich method. |
| first_indexed | 2024-03-09T14:16:22Z |
| format | Article |
| id | doaj.art-130353e16b11428d810b06b9a206cf2f |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-09T14:16:22Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-130353e16b11428d810b06b9a206cf2f2023-11-29T01:16:37ZengAIMS PressMathematics in Engineering2640-35012023-10-015511910.3934/mine.2023089Kolmogorov variation: KAM with knobs (à la Kolmogorov)Marco Sansottera0Veronica Danesi11. Rocketloop GmbH, Hansaallee 154, 60320 Frankfurt, Germany2. Department of Mathematics, University of Rome "Tor Vergata", via della Ricerca Scientifica 1, 00133 Rome, ItalyIn this paper we reconsider the original Kolmogorov normal form algorithm [26] with a variation on the handling of the frequencies. At difference with respect to the Kolmogorov approach, we do not keep the frequencies fixed along the normalization procedure. Besides, we select the frequencies of the final invariant torus and determine a posteriori the corresponding starting ones. In particular, we replace the classical translation step with a change of the frequencies. The algorithm is based on the original scheme of Kolmogorov, thus exploiting the fast convergence of the Newton-Kantorovich method.https://www.aimspress.com/article/doi/10.3934/mine.2023089?viewType=HTMLkolmogorov normal formperturbation theorykam theorem |
| spellingShingle | Marco Sansottera Veronica Danesi Kolmogorov variation: KAM with knobs (à la Kolmogorov) Mathematics in Engineering kolmogorov normal form perturbation theory kam theorem |
| title | Kolmogorov variation: KAM with knobs (à la Kolmogorov) |
| title_full | Kolmogorov variation: KAM with knobs (à la Kolmogorov) |
| title_fullStr | Kolmogorov variation: KAM with knobs (à la Kolmogorov) |
| title_full_unstemmed | Kolmogorov variation: KAM with knobs (à la Kolmogorov) |
| title_short | Kolmogorov variation: KAM with knobs (à la Kolmogorov) |
| title_sort | kolmogorov variation kam with knobs a la kolmogorov |
| topic | kolmogorov normal form perturbation theory kam theorem |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023089?viewType=HTML |
| work_keys_str_mv | AT marcosansottera kolmogorovvariationkamwithknobsalakolmogorov AT veronicadanesi kolmogorovvariationkamwithknobsalakolmogorov |