In order to describe the dynamics of the complex Hénon map , where has an attractive fixed point, we build a global topological model . In this model is the complement in of a cone over a solenoid lying in the unit 3-sphere, and is a map given in spherical coordinates by , where is a solenoidal map of degree two. Then we prove the existence of a constant such that any Hénon map with is conjugate to our model .
Cite this article
Sylvain Bonnot, Topological model for a class of complex Hénon mappings. Comment. Math. Helv. 81 (2006), no. 4, pp. 827–857DOI 10.4171/CMH/76