Gluing Dynamics: $\varepsilon$-Precision in Solving a Non-Archimedean Inverse Problem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911513137119232 |
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| author | Nopal-Coello Víctor Pérez-Buendía Rogelio, J. |
| author_facet | Nopal-Coello Víctor Pérez-Buendía Rogelio, J. |
| contents | This research proposes a new method for approximating the solution of the inverse problem of finding a rational function that generates known local dynamics within distinct, disjoint closed balls in non-Archimedean fields. Although our approach is not directly influenced by Runge's theorem for approximating analytic maps in complex settings, it shares similarities by adapting these ideas to the non-Archimedean context. We aim to connect local dynamic behaviors, similar to dynamic surgery, without using quasiconformal but rational mappings. Our main theorem and corollaries present an algorithmic technique to construct a rational function, denoted as \(F_\varepsilon\), that synthesizes specified local dynamics with an \(\varepsilon\)-precision parameter globally. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04363 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gluing Dynamics: $\varepsilon$-Precision in Solving a Non-Archimedean Inverse Problem Nopal-Coello Víctor Pérez-Buendía Rogelio, J. Dynamical Systems 11S82, 37P05, 37P20 This research proposes a new method for approximating the solution of the inverse problem of finding a rational function that generates known local dynamics within distinct, disjoint closed balls in non-Archimedean fields. Although our approach is not directly influenced by Runge's theorem for approximating analytic maps in complex settings, it shares similarities by adapting these ideas to the non-Archimedean context. We aim to connect local dynamic behaviors, similar to dynamic surgery, without using quasiconformal but rational mappings. Our main theorem and corollaries present an algorithmic technique to construct a rational function, denoted as \(F_\varepsilon\), that synthesizes specified local dynamics with an \(\varepsilon\)-precision parameter globally. |
| title | Gluing Dynamics: $\varepsilon$-Precision in Solving a Non-Archimedean Inverse Problem |
| topic | Dynamical Systems 11S82, 37P05, 37P20 |
| url | https://arxiv.org/abs/2311.04363 |