Brody curves in complicated sets

TL;DR

This paper demonstrates the existence of a special type of injective Brody leaf within the boundary foliation of non-escaping points for specific Hénon maps in complex dynamics.

Contribution

It establishes the presence of an injective Brody leaf in the boundary foliation of non-escaping points for certain Hénon mappings, advancing understanding of complex dynamical systems.

Findings

Existence of an injective Brody leaf in the boundary foliation.

Identification of such leaves in the context of Hénon mappings.

Contribution to the understanding of complex dynamics in $\,\mathbb{P}^2$.

Abstract

We prove the existence of a leaf, which is injective Brody in $\mathbb{P}^2$, in the foliation of the boundary of the set of non-escaping points for certain H\'enon mappings.