A hyperbolic-distance inequality for holomorphic maps

TL;DR

This paper establishes a hyperbolic-distance inequality for holomorphic self-maps of the disc, showing how small perturbations of points imply the map is close to the identity, enhancing understanding of holomorphic dynamics.

Contribution

The paper introduces a new inequality relating hyperbolic distances for holomorphic maps, providing a quantitative measure of how perturbations affect the map's proximity to the identity.

Findings

Inequality quantifies closeness to identity for perturbed points

Provides bounds on holomorphic self-maps of the disc

Enhances understanding of holomorphic dynamics near identity

Abstract

We prove an inequality which quantifies the idea that a holomorphic self-map of the disc that perturbs two points is close to the identity function.