Let f : Cn → Cn, with n ≥ 2, be a biholomorphism, and let Cn be a compact f -invariant set such that f |? is partially hyperbolic. We give equivalent conditions for hyperbolicity on ?. In particular, for generalized Hènon maps with dominated splitting in the Julia set J, we characterize the hyperbolicity of J.
- Holomorphic functions. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 37D10
- Invariant manifold theory
- Partially hyperbolic systems and dominated splittings