JournalsjemsVol. 23, No. 9pp. 3075–3128

Structure of partially hyperbolic Hénon maps

  • Mikhail Lyubich

    Stony Brook University, USA
  • Han Peters

    University of Amsterdam, Netherlands
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Abstract

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 J=JJ = J^\star and the dynamics on JJ 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. 3075–3128

DOI 10.4171/JEMS/1074