论文信息 - A Local-Global Criterion for Dynamics on P^1

A Local-Global Criterion for Dynamics on P^1

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.

Joseph H. Silverman | Jos'e Felipe Voloch

[1] M. Baker. A finiteness theorem for canonical heights attached to rational maps over function fields , 2006, math/0601046.

[2] Victor Scharaschkin,et al. Local -global problems and the Brauer -Manin obstruction. , 1999 .

[3] The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields , 2006, math/0612263.

[4] Joseph H. Silverman,et al. Primitive divisors in arithmetic dynamics , 2009, Mathematical Proceedings of the Cambridge Philosophical Society.

[5] K. Zsigmondy,et al. Zur Theorie der Potenzreste , 1892 .

[6] Joseph H. Silverman,et al. Integer points, Diophantine approximation, and iteration of rational maps , 1993 .

[7] Joseph H. Silverman,et al. Wieferich's criterion and the abc-conjecture , 1988 .

[8] Joseph H. Silverman,et al. On a Dynamical Brauer-Manin Obstruction , 2008 .

[9] A. Schinzel. Primitive divisors of the expression An - Bn in algebraic number fields. , 1968 .