Connected escaping sets of exponential maps

TL;DR

This paper investigates the connectedness of escaping sets in exponential maps, demonstrating that for many parameters, these sets are connected, especially when the singular value tends to infinity.

Contribution

It establishes the connectedness of escaping sets for a broad class of exponential maps, including those with escaping singular values.

Findings

Escaping sets are connected for many parameters.

Includes all parameters with singular value escaping to infinity.

Provides new insights into the structure of exponential map dynamics.

Abstract

We show that for many complex parameters a, the set of points that converge to infinity under iteration of the exponential map f(z)=e^z+a is connected. This includes all parameters for which the singular value escapes to infinity under iteration.