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arXiv · 0806.2580

A Local-Global Criterion for Dynamics on P^1

Joseph H. Silverman·José Felipe Voloch
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Abstract

Let K be a number field or a function field, let F:P^1 --> P^1 be a rational map of degree at least two defined over K, let P be a point in P^1(K) having infinite F-orbit, and let Z be a finite subset of Z. We prove a local-global criterion for the intersection of the F-orbit of P and the finite set Z. This is a special case of a dynamical Brauer-Manin criterion suggested by Hsia and Silverman.

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Joseph H. Silverman, José Felipe Voloch. 2008-06-16. A Local-Global Criterion for Dynamics on P^1. https://doi.org/10.4064/aa137-3-8

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