35 citations · 45 across the 8 of their papers we have counts for
6 papers · 1 filter
Eventually stable rational functions
Rafe Jones, Alon Levy
For a field K, rational function phi in K(z) of degree at least two, and alpha in P^1(K), we study the polynomials in K[z] whose roots are given by the solutions to phi^n(z) = alph…
Finite ramification for preimage fields of postcritically finite morphisms
Andrew Bridy, Patrick Ingram, Rafe Jones +5
Given a finite endomorphism of a variety defined over the field of fractions of a Dedekind domain, we study the extension $K(φ^{-\infty}(α)) : = \bigcup_{n \geq 1} K(φ^…
Isolated Periodic Points in Several Nonarchimedean Variables
Alon Levy
Let where is a complete valued field. If is a fixed point, such that the action of on has eigenvalues $λ_{1}, \ld…
The McMullen Map in Positive Characteristic
Alon Levy
McMullen proved the moduli space of complex rational maps can be parametrized by the spectrum of all periodic-point multipliers up to a finite amount of data, with the well-underst…
Uniform bounds for pre-periodic points in families of twists
Alon Levy, Michelle Manes, Bianca Thompson
Let phi be a morphism of projective N-space defined over a number field K. We prove that there is a bound B depending only on phi such that every twist of phi has no more than B K-…
Attracting cycles in p-adic dynamics and height bounds for post-critically finite maps
Robert L. Benedetto, Patrick Ingram, Rafe Jones +1
A rational function of degree at least two with coefficients in an algebraically closed field is post-critically finite (PCF) if all of its critical points have finite forward orbi…