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

Fuente: arXiv
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Main Authors: Nopal-Coello, Víctor, Pérez-Buendía, Rogelio, J.
Format: Preprint
Published: 2023
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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