# Topological model for a class of complex Hénon mappings

### Sylvain Bonnot

Stony Brook University, United States

## Abstract

In order to describe the dynamics of the complex Hénon map $H_{a,c}:(xy )↦(P_{c}(x)−ayx )$, where $P_{c}:z↦z_{2}+c$ has an attractive fixed point, we build a global topological model $(g,Y)$. In this model $Y$ is the complement in $R_{4}$ of a cone over a solenoid lying in the unit 3-sphere, and $g:Y→Y$ is a map given in spherical coordinates by $g(r,θ)=(r_{2},σ(θ))$, where $σ$ is a solenoidal map of degree two. Then we prove the existence of a constant $ε>0$ such that any Hénon map $H_{a,c}$ with $0<∣a∣<ε$ is conjugate to our model $(g,Y)$.

## Cite this article

Sylvain Bonnot, Topological model for a class of complex Hénon mappings. Comment. Math. Helv. 81 (2006), no. 4, pp. 827–857

DOI 10.4171/CMH/76