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In this work, we introduce "non-archimedean surgery" (na-surgery), anadaptation of quasiconformal surgery from the complex plane to non-archimedeanfields. Through this approach, we construct rational functions that approximatelocal dynamics in non-archimedean spaces and advance an algorithmic solution tothe Inverse Problem in arithmetic dynamics. Our na-surgery method permitscontrolled modifications of dynamical systems in non-archimedean contexts,enabling us to synthesize global dynamics from local behaviors with precisionup to an \(\varepsilon\)-parameter. This development furnishes a systematicmethod for both the construction and examination of dynamical systems withinnon-archimedean frameworks, enhancing the toolkit for research in arithmeticdynamics.

Gluing Local Dynamics: An Algorithmic Surgery Method in Non-archimedean Fields