Equivalent conditions for hyperbolicity on partially hyperbolic holomorphic map Francisco Valenzuela-Henriquez 37D1037D3032A10invariant manifold theorypartially hyperbolic systems and dominated splittingsholomorphic functions Let $f: \mathbb{C}^n \to \mathbb{C}^n$, with $n \geq 2$, be a biholomorphism, and let $\Lambda \subseteq \mathbb{C}^n$ be a compact $f$-invariant set such that $f|\Lambda$ is partially hyperbolic. We give equivalent conditions for hyperbolicity on $\Lambda$. In particular, for generalized H\'enon maps with dominated splitting in the Julia set $J$, we characterize the hyperbolicity of $J$. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4375 10.1512/iumj.2011.60.4375 en Indiana Univ. Math. J. 60 (2011) 1363 - 1392 state-of-the-art mathematics http://iumj.org/access/