Bounded Height in Families of Dynamical Systems
نویسندگان
چکیده
Let a, b ∈ Q be such that exactly one of a and b is an algebraic integer, and let ft(z) := z 2 + t be a family of polynomials parametrized by t ∈ Q. We prove that the set of all t ∈ Q for which there exist m,n ≥ 0 such that f t (a) = f t (b) has bounded height. This is a special case of a more general result supporting a new bounded height conjecture in arithmetic dynamics.
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تاریخ انتشار 2017