The escaping set of the exponential

TL;DR

This paper proves that the set of points in the complex plane that tend to infinity under repeated exponential function application is a connected set, revealing new insights into the structure of exponential dynamical systems.

Contribution

It establishes the connectedness of the escaping set for the exponential map, a significant result in complex dynamics.

Findings

The escaping set is connected.

Points tend to infinity under iteration form a connected subset.

Provides new understanding of exponential map dynamics.

Abstract

We show that the points that converge to infinity under iteration of the exponential map form a connected subset of the complex plane.