Benjamin Hutz

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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)
This article examines dynamical systems on a class of K3 surfaces in P×P with an infinite automorphism group. In particular, this article develops an algorithm to find Q-rational periodic points using information over Fp for various primes p. This algorithm is then optimized to examine the growth of the average number of cycles versus p and to determine the(More)
We consider dynamical systems arising from iterating a morphism of a projective variety defined over the field of fractions of a discrete valuation ring. Our goal is to obtain information about the dynamical system over the field of fractions by studying the dynamical system over the residue field. In particular, we aim to bound the possible primitive(More)
The purpose of this note is give some evidence in support of conjectures of Poonen, and Morton and Silverman, on the periods of rational numbers under the iteration of quadratic polynomials. Suppose that φc(z) = z 2 + c, where c ∈ Q. We will say that α ∈ P1(Q) is a periodic point with exact period n for φc if φ n c (α) = α, while φ m c (α) 6= α for 0 < m <(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)