On the dimension of points which escape to infinity at given rate under exponential iteration

TL;DR

This paper investigates the Hausdorff and packing dimensions of points escaping to infinity at specified rates under non-autonomous exponential map iteration, extending previous results and addressing open questions about annular itineraries.

Contribution

It generalizes prior work on exponential map dynamics by analyzing dimensions of escaping points under non-autonomous iteration and resolving an open question about annular itineraries.

Findings

Determined Hausdorff and packing dimensions of escaping sets.

Extended results to non-autonomous exponential maps.

Answered open question on annular itineraries.

Abstract

We prove a number of results concerning the Hausdorff and packing dimension of sets of points which escape (at least in average) to infinity at a given rate under non-autonomous iteration of exponential maps. In particular, we generalize the results proved by Sixsmith in 2016 and answer his question on annular itineraries for exponential maps.