The entropy of holomorphic correspondences: exact computations and rational semigroups

TL;DR

This paper investigates two notions of topological entropy for holomorphic correspondences, providing exact calculations for rational semigroups and revealing a connection between the two entropy concepts.

Contribution

It identifies a class of holomorphic correspondences where Dinh-Sibony entropy equals the known upper bound, enabling exact entropy computation for rational semigroups.

Findings

Exact entropy computation for rational semigroups

Identification of a class where Dinh-Sibony entropy matches the upper bound

Exploration of the relationship between Friedland and Dinh-Sibony entropy notions

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.