A Local-Global Criterion for Dynamics on P^1

Details A Local-Global Criterion for Dynamics on P^1 A Local-Global Criterion for Dynamics on P^1

2008-06-16

arxiv.org/abs/0806.2580v1

Acta Arithmetica 137.3 (2009), 285--294

Mathematics

Number Theory

10 pages

Scientific paper

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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