Bifurcation for families of Ahlfors island maps

TL;DR

This paper extends stability characterizations to Ahlfors island maps, including meromorphic maps, and shows that J-stability is dense among finite type maps, advancing understanding of dynamical stability in complex analysis.

Contribution

It generalizes existing stability criteria to a broader class of maps and establishes the density of J-stability for finite type maps.

Findings

Extended stability characterization to Ahlfors island maps.

Proved density of J-stability for finite type maps.

Included all meromorphic maps as a special case.

Abstract

We extend Ma\~n\'e-Sad-Sullivan and Lyubich's equivalent characterization of stability to the setting of Ahlfors island maps, which include notably all meromorphic maps. As a consequence we also obtain the density of $J$-stability for finite type maps in the sense of Epstein.