Non-bulging Baker domains for transcendental skew products

TL;DR

This paper investigates the nature of Baker domains in transcendental skew products, revealing that their bulging behavior depends on higher order terms, unlike polynomial skew products where all such domains bulge.

Contribution

It demonstrates that Baker domains in transcendental skew products can either bulge or not, based on higher order terms, contrasting with polynomial cases.

Findings

Baker domains can either bulge or not in transcendental skew products.

Bulging depends on higher order terms in the map.

Contrast with polynomial skew products where all bounded Fatou components bulge.

Abstract

In this paper we show that Baker domains of transcendental skew products can either bulge or not, depending on the higher order terms. This is in contrast to polynomial skew products where all Fatou components with bounded orbits of an invariant attracting fiber do bulge.