Equivalent conditions for hyperbolicity on partially hyperbolic holomorphic map

Abstract

Let $f:\mathbb{C}\sp n\to\mathbb{C}\sp n$, $n\ge 2$, be a biholomorphism and let $Λ\subseteq \mathbb{C}\sp n$ be a compact $f$-invariant set such that $f|\Lambda$ is partially hyperbolic. We give equivalent conditions to hyperbolicity on $\Lambda$. In the particular case of generalized Hénon map with dominated splitting in the Julia set $J$, we characterize the hyperbolicity of $J$.

References in corpus (2)

• Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents
• Stable manifolds of holomorphic diffeomorphisms