Equidistribution of graphs of holomorphic correspondences

Abstract

Let $X$ be a compact Riemann surface. Let $f$ be a holomorphic self-correspondence of $X$ with dynamical degrees $d_1$ and $d_2$. Assume that $d_1\ne d_2$ or $f$ is non-weakly modular. We show that the graphs of the iterates $f^n$ of $f$ are equidistributed exponentially fast with respect to a positive closed current in $X\times X$.

References in corpus (2)

• Distribution des preimages et des points periodiques d'une correspondance polynomiale
• Equidistribution for matings of quadratic maps with the Modular group