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- Robert L Benedetto, Dragos Ghioca, Benjamin Hutz, Pär Kurlberg, Thomas Scanlon, Thomas J Tucker +7 others
- 2011

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)

The behavior under iteration of the critical points of a polynomial map plays an essential role in understanding its dynamics. We study the special case where the forward orbits of the critical points are finite. Thurston's theorem tells us that fixing a particular critical point portrait and degree leads to only finitely many possible polynomials (up to… (More)

- Rafe Jones, Jordan Cahn, Jacob Spear, Robert Benedetto, Patrick Ingram, Alon Levy +12 others
- 2014

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)

- Xander Faber, Benjamin Hutz
- 2010

For a quadratic endomorphism of the affine line defined over the rationals, we consider the problem of bounding the number of rational points that eventually land at the origin after iteration. In the article " Uniform Bounds on Pre-Images Under Quadratic Dynamical Systems, " by the present authors and five others, it was shown that the number of rational… (More)

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