Critical locus for H\'enon maps in an HOV region

TL;DR

This paper extends the understanding of the critical locus for complex Hénon maps, showing that Firsova's characterization applies in a broader HOV-like region beyond small perturbations.

Contribution

It generalizes the characterization of the critical locus for Hénon maps to a larger parameter region using non-perturbative techniques.

Findings

Firsova's characterization applies in a larger HOV-like region.

The techniques used are non-perturbative.

The results extend the understanding of complex Hénon maps.

Abstract

We prove that the characterization of the critical locus for complex H\'enon maps that are small perturbations of quadratic polynomials with disconnected Julia sets given by Firsova holds in a much larger HOV-like region from the complex horseshoe locus. The techniques of this paper are non-perturbative.