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Non-Archimedean connected Julia sets with branching. (English) Zbl 1391.37083

Summary: We construct the first examples of rational functions defined over a non-archimedean field with a certain dynamical property: the Julia set in the Berkovich projective line is connected but not contained in a line segment. We also show how to compute the measure-theoretic and topological entropy of such maps. In particular, we give an example for which the measure-theoretic entropy is strictly smaller than the topological entropy, thus answering a question of C. Favre and J. Rivera-Letelier [C. R., Math., Acad. Sci. Paris 339, No. 4, 271–276 (2004; Zbl 1052.37039)].

MSC:

37P40 Non-Archimedean Fatou and Julia sets
37P20 Dynamical systems over non-Archimedean local ground fields
37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps
11S85 Other nonanalytic theory
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets

Citations:

Zbl 1052.37039
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References:

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