# Dynamics of transcendental H\'enon maps-II

## TL;DR

This paper explores the dynamics of transcendental Hénon maps, showing they always exhibit complex behavior with non-empty Julia sets, including periodic and escaping orbits, extending the understanding of polynomial Hénon maps to a broader class.

## Contribution

It proves that transcendental Hénon maps always have non-trivial dynamics, including the existence of periodic and escaping orbits, and non-empty Julia sets.

## Key findings

- Existence of both periodic and escaping orbits
- Julia sets are non-empty and perfect
- Transcendental Hénon maps exhibit complex dynamical behavior

## Abstract

Transcendental H\'enon maps are the natural extensions of the well investigated complex polynomial H\'enon maps to the much larger class of holomorphic automorphisms. We prove here that transcendental H\'enon maps always have non-trivial dynamical behavior, namely that they always admit both periodic and escaping orbits, and that their Julia sets are non-empty and perfect.