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The aim of this paper is to show $J$ -stability of expanding rational maps over an algebraically closed, complete and non-Archimedean field of characteristic zero. More precisely, we will show… Click to show full abstract
The aim of this paper is to show $J$ -stability of expanding rational maps over an algebraically closed, complete and non-Archimedean field of characteristic zero. More precisely, we will show that for any expanding rational map, there exists a neighborhood of it such that the dynamics on the Julia set of any rational map in the neighborhood is the same as the dynamics of the expanding rational map as a non-Archimedean analogue of a corollary of Mañé, Sad and Sullivan’s result [On the dynamics of rational maps. Ann. Sci. Éc. Norm. Supér. (4) 16 (1983), 193–217] in complex dynamics.
Journal Title: Ergodic Theory and Dynamical Systems
Year Published: 2017
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