We describe the structure of “substantially dissipative” complex Hénon maps admitting a dominated splitting on the Julia set. We prove that the Fatou set consists of only finitely many components, each either attracting or parabolic periodic. In particular, there are no wandering components and no rotation domains. Moreover, we show that and the dynamics on is hyperbolic away from parabolic cycles.
Cite this article
Mikhail Lyubich, Han Peters, Structure of partially hyperbolic Hénon maps. J. Eur. Math. Soc. 23 (2021), no. 9, pp. 3075–3128DOI 10.4171/JEMS/1074