49 citations · 161 across the 26 of their papers we have counts for
38 papers
Abelian dynamical Galois groups over global function fields
Andrea Ferraguti, Patrick Ingram, Carlo Pagano
We establish a function field analogue of a recent conjecture of Andrews--Petsche. Our main result characterizes abelian dynamical Galois groups to be precisely the isotrivial ones…
An asymptotic for sums of Lyapunov exponents in families
Patrick Ingram, David Jaramillo-Martinez, Jorge Mello
Let f_t be a meromorphic family of endomorphisms of P^N_C of degree at least 2, and let L(f_t) be the sum of Lyapunov exponents associated to f_t. Favre showed that L(f_t)=L(f)\log…
A remark on post-critically finite compositions of polynomials
Benjamin Fraser, Patrick Ingram
The second author proved that the set of post-critically finite polynomials of given degree is a set of bounded height, up to change of variables. Motivated by an observation about…
Explicit canonical heights for divisors relative to endomorphisms of
Patrick Ingram
Given an endomorphism f of projective space, we exhibit explicit bounds on the difference between the naive height of a divisor and its canonical height relative to f.
Variation of the canonical height in a family of polarized dynamical systems
Patrick Ingram
Call and Silverman introduced the canonical height associated to a polarized dynamical system, that is, an endomorphism of a projective variety and an ample line bundle which pulls…
Solutions to difference equations have few defects
Patrick Ingram
We demonstrate a strong form of Nevanlinna's Second Main Theorem for solutions to difference equations f(z+1)=R(z, f(z)), with the coefficients of R growing slowly relative to f, a…