2024/05/23 by Noytaptim, Chatchai, Zhong, Xiao
#37P05 #37P30 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2405.15104
Answering a question asked by Hsia and Tucker in their paper on the finiteness of greatest common divisors of iterates of polynomials, we prove that if f, g ∈ ℂ(X) are compositionally independent rational functions and c ∈ ℂ(X), then there are at most finitely many λ∈ℂ with the property that there is an n such that fn(λ) = gn(λ) = c(λ), except for a few families of f, g ∈ Aut(ℙ1_ℂ) which gives counterexamples.