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Let K be a number field, let ϕ ∈ K (t) be a rational map of degree at least 2, and let α, β ∈ K. We show that if α is not in the forward orbit of β, then there is a positive proportion of primes p of K such that α mod p is not in the forward orbit of β mod p. Moreover, we show that a similar result holds for several maps and several points. We also present(More)
For a morphism f : PN → PN , the points whose forward orbit by f is finite are called preperiodic points for f . This article presents an algorithm to effectively determine all the rational preperiodic points for f defined over a given number field K. This algorithm is implemented in the open-source software Sage for Q. Additionally, the notion of a(More)
This article addresses the existence of Q-rational periodic points for morphisms of projective space. In particular, we construct an infinitely family of morphisms on P N where each component is a degree 2 homogeneous form in N +1 variables which has a Q-periodic point of primitive period (N+1)(N+2) 2 + ¨ N−1 2 ˝. This result is then used to show that for N(More)