Given an affine variety X, a morphism ϕ:X→X, a point α∈X, and a Zariski-closed subset V of X, we show that the forward ϕ-orbit of α meets V in at most finitely many infinite arithmetic progressions, and the remaining points lie in a set of Banach density zero. This may...
Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...