English

A Local-Global Criterion for Dynamics on P^1

Number Theory 2015-05-13 v1 Dynamical Systems

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.

Keywords

Cite

@article{arxiv.0806.2580,
  title  = {A Local-Global Criterion for Dynamics on P^1},
  author = {Joseph H. Silverman and José Felipe Voloch},
  journal= {arXiv preprint arXiv:0806.2580},
  year   = {2015}
}

Comments

10 pages

R2 v1 2026-06-21T10:51:01.719Z