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arXiv · 2311.04363

Gluing Dynamics: $\varepsilon$-Precision in Solving a Non-Archimedean Inverse Problem

Nopal-Coello·Víctor·Pérez-Buendía·J. Rogelio
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Abstract

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.

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Nopal-Coello, Víctor, Pérez-Buendía, J. Rogelio. 2023-11-07. Gluing Dynamics: $\varepsilon$-Precision in Solving a Non-Archimedean Inverse Problem. https://doi.org/10.1007/s40590-025-00730-y

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