Abstract: I will give a brief introduction to an open problem in arithmetic dynamics and some related results. This problem is motivated by a result of Amoroso and Dvornicich (2000), which states that the (absolute logarithmic) Weil height of $\alpha \in \mathbb{Q}^{ab}$, where $\alpha$ is nonzero and is not a root of unity, is bounded below. The open problem, which we refer to as dynamical Amoroso-Dvornicich, asks if we can prove an analogous result in the dynamical setting. In the dynamical setting, the Weil height is replaced by the dynamical height for a polynomial over a number field, and the roots of unity are replaced with (pre)periodic points of the polynomial.
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