Speeds of convergence of orbits of non-elliptic semigroups of holomorphic self-maps of the unit disc

TL;DR

This paper introduces three measures of orbit convergence speeds for non-elliptic semigroups of holomorphic self-maps of the unit disc, exploring their interrelations and implications.

Contribution

It defines and analyzes total, orthogonal, and tangential speeds of orbits, providing new insights into their relationships and what can be inferred from these quantities.

Findings

Relationships among the three speed measures are established.

Insights into the dynamics of non-elliptic semigroups are gained.

Potential applications to understanding orbit convergence behavior.

Abstract

We introduce three quantities related to orbits of non-elliptic continuous semigroups of holomorphic self-maps of the unit disc, the total speed, the orthogonal speed and the tangential speed and show how they are related and what can be inferred from those.