Title: Equivalent conditions for hyperbolicity on partially hyperbolic holomorphic map

Authors: Francisco Valenzuela-Henriquez

Issue: Volume 60 (2011), Issue 4, 1363-1392


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 $J$.