Variation of Periods Modulo p in Arithmetic Dynamics

الأصل · EN

Let F: V --> V be a self-morphism of a quasiprojective variety defined over a number field K and let P be a point in V(K) with infinite orbit under iteration of F. For each prime ideal p of good reduction, let mₚ(F,P) be the size of the F-orbit of the reduction of P modulo p. Fix any e > 0. We show that for almost all primes p, in the sense of analytic density, the orbit size mₚ(F,P) is larger than (log(N(p)))(1-e), where N(p) is the norm of the ideal p.