Abstract: A rational map is conservative if all critical points are fixed. Conservative maps are the simplest examples of post-critically finite maps, making them a family of interest in arithmetic dynamics. Silverman found a trivial family of conservative polynomials such that the height of the polynomials tends to 0 as the degree tends to infinity. This motivated Silverman to pose the question, do the heights of all normalized conservative polynomials grow proportionally to the heights of the trivial family? By manipulating the family of dynamical Belyi polynomials we are able to answer this question in the negative.

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