2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115646Let $\MP_d$ denote the space of polynomials $f: \C \to \C$ of degree $d\geq 2$, modulo conjugation by $\Aut(\C)$. Using properties of polynomial trees (as introduced in [DM, math.DS/0608759]), we show that if $f_n$ is a divergent sequence of polynomials in $\MP_d$, then any subsequential limit of the measures of maximal entropy $m(f_n)$ will have finite support. With similar techniques, we observe that the iteration maps $\{\MPbar_d \dashrightarrow \MPbar_{d^n}: n\geq 1\}$ between GIT-compactifications can be resolved simultaneously with only finitely many blow-ups of $\MPbar_d$.15 pages, for the Proceedings of the Holomorphic Dynamics Workshop, in celebration of J. Milnor's 75th birthdayDynamical SystemsComplex Variablestext