Modèle topologique pour des applications de Hénon complexes

In order to describe the dynamics of the complex Hénon map Ha,c:(xy)↦(Pc(x)−ayx), where Pc:z↦z2+c has an attractive fixed point, we build a topological model (g,Y). In this model Y is the complement in R4 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)=(r2,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 Ha,c with 0<|a|<ε is conjugate to our model (g,Y). To cite this article: S. Bonnot, C. R. Acad. Sci. Paris, Ser. I 340 (2005).