Semigroup representations in holomorphic dynamics
Carlos Cabrera, Peter Makienko, Peter Plaumann
TL;DR
This paper explores how semigroup theory and its representation can describe automorphisms in holomorphic dynamics, extending classical theorems to correspondences and revealing new structural insights.
Contribution
It introduces a novel application of semigroup representation theory to holomorphic dynamical systems and extends Schreier's theorem to correspondences.
Findings
Semigroup representations relate to holomorphic dynamics constructions
Extended Schreier's theorem to correspondences
Provided examples illustrating the theory
Abstract
We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show, with some examples, that representation theory of semigroups is related to usual constructions in holomorphic dynamics. The main tool for our discussion is a theorem due to Schreier. We extend this theorem, and our results in semigroups, to the setting of correspondences and holomorphic correspondences.
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