MME for Mating Correspondences

Abstract

We use the measure theoretical entropy from Vivas-Sirvent and the topological entropies from Dinh-Sibony and Kelly-Tennant to prove that the equidistribution measures ${\mu }_{-}$ and ${\mu }_{+}$ found by the author maximize entropy for the $1$-parameter family $\{{\mathcal{F}}_a{\}}_a$ studied by Bullett-Lomonaco. We find as well a measure of maximal entropy for the composition of two deleted covering correspondences studied by Bullett.