The entropy of holomorphic correspondences: exact computations and rational semigroups

Abstract

We study two notions of topological entropy of correspondences introduced by Friedland and Dinh-Sibony. Upper bounds are known for both. We identify a class of holomorphic correspondences whose entropy in the sense of Dinh-Sibony equals the known upper bound. This provides an exact computation of the entropy for rational semigroups. We also explore a connection between these two notions of entropy.

18 pages; added references; added a new expository section (Subsection 1.1) and further exposition in Section 5; to appear in Ann. Acad. Sci. Fennicae