In the 60’s, Brolin proved that preimages under a polynomial of degree \(d\geq 2\) equidistribute with respect to certain measure on \(\mathbb{C}\). Since then, equidistribution became an interesting property to study. It was proven by Freire-Lopes-Mañé and by Ljubich that this holds for rational maps when regarded as dynamical systems over the Riemann sphere, and this was later generalized to higher dimension by Briend-Duval, to non-archimedian fields by Favre-Rivera-Letelier, as well to modular correspondences by Clozel-Oh-Ullmo, to non weakly-modular correspondences by Dinh-Kauffman-Wu, to holomorphic correspondences having a repeller by Bharali-Sridharan, and so on.

In this talk, we will talk about a 1-parameter family of holomorphic correspondences \(\lbrace\mathcal{F}_a\rbrace_{a\in\mathcal{K}}\) given by the equation

\[\left(\frac{az+1}{z+1}\right)^2+\left(\frac{az+1}{z+1}\right)\left(\frac{aw-1}{w-1}\right)+\left(\frac{aw-1}{w-1}\right)^2=3.\]

We will explain why this family does not fit the conditions for the results above, and we will use the description given by Bullett-Lomonaco of these correspondences to show that equidistribution holds. We will also talk about the equidistribution of periodic points.