On periodic approximate solutions of dynamical systems with a quadratic right-hand side
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909409361264640 |
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| author | Malykh, Mikhail Sevastianov, Leonid |
| author_facet | Malykh, Mikhail Sevastianov, Leonid |
| contents | Difference schemes are considered for dynamical systems $ \dot x = f (x) $ with a quadratic right-hand side, which have $t$-symmetry and are reversible. Reversibility is interpreted in the sense that the Cremona transformation is performed at each step in the calculations using a difference scheme. The inheritance of periodicity and the Painlevé property by the approximate solution is investigated. In the computer algebra system Sage, such values are found for the step $ Δt $, for which the approximate solution is a sequence of points with the period $ n \in \mathbb N $. Examples are given and hypotheses about the structure of the sets of initial data generating sequences with the period $ n $ are formulated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_14507 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On periodic approximate solutions of dynamical systems with a quadratic right-hand side Malykh, Mikhail Sevastianov, Leonid Classical Analysis and ODEs Dynamical Systems Difference schemes are considered for dynamical systems $ \dot x = f (x) $ with a quadratic right-hand side, which have $t$-symmetry and are reversible. Reversibility is interpreted in the sense that the Cremona transformation is performed at each step in the calculations using a difference scheme. The inheritance of periodicity and the Painlevé property by the approximate solution is investigated. In the computer algebra system Sage, such values are found for the step $ Δt $, for which the approximate solution is a sequence of points with the period $ n \in \mathbb N $. Examples are given and hypotheses about the structure of the sets of initial data generating sequences with the period $ n $ are formulated. |
| title | On periodic approximate solutions of dynamical systems with a quadratic right-hand side |
| topic | Classical Analysis and ODEs Dynamical Systems |
| url | https://arxiv.org/abs/2104.14507 |