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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)
Research Interests • Galois theory and irreducibility of polynomials (particularly involving iterated morphisms) • Discrete dynamics (particularly iteration of rational functions over global and finite fields) • Automorphism groups of rooted trees and iterated monodromy groups • Elliptic curves and torsion fields • Recurrence sequences Perfect powers in(More)
We consider the dynamical system created by iterating a morphism of a projective variety over the field of fractions of a discrete valuation ring. In the case of good reduction, we study the primitive period of a periodic point on the residue field. We start by defining good reduction, examine the behavior of primitive periods under good reduction, and end(More)