A quantitative estimate for quasiintegral points in orbits

Abstract

Let ϕ(z) ∈ K(z) be a rational function of degree d ≥ 2 defined over a number field whose second iterate ϕ 2 (z) is not a polynomial, and let α ∈ K. The second author previously proved that the forward orbit O ϕ (α) contains only finitely many quasi-S-integral points. We give an explicit upper bound for the number of such points.