One Parameter Semigroups in Two Complex Variables

TL;DR

This paper extends the theory of embedding discrete self-maps into continuous semigroups from one complex variable to two complex variables, specifically for maps of the unit ball.

Contribution

It generalizes embedding results for self-maps from one complex variable to two complex variables under certain conditions.

Findings

Extended embedding results to two complex variables.

Identified conditions for embedding in higher dimensions.

Contributed to the understanding of complex dynamical systems.

Abstract

For self maps of the disk, it can be shown that under the right conditions one can embed a discrete iteration of the map into a continuous semigroup. In this article we extend these results to two complex variables for maps of the unit ball into itself under some restricted conditions.