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Register a new userAn Ahlfors Islands Theorem for non-archimedean meromorphic functions
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Authors
Robert L. Benedetto
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We present a p-adic and non-archimdean version of the Five Islands Theorem for meromorphic functions from Ahlfors theory of covering surfaces. In the non-archimedean setting, the theorem requires only four islands, with explicit constants. We present examples to show that the constants are sharp and that other hypotheses of the theorem cannot be removed. This paper extends an earlier theorem of the author for holomorphic functions.
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Let K be a non-archimedean field, and let f in K(z) be a polynomial or rational function of degree at least 2. We present a necessary and sufficient condition, involving only the fixed points of f and their preimages, that determines whether or not the dynamical system f on P^1 has potentially good reduction.
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