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arXiv · 1005.2206

Equivalent conditions for hyperbolicity on partially hyperbolic holomorphic map

Francisco Valenzuela Henriquez
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Abstract

Let $f:\mathbb{C}\sp n\to\mathbb{C}\sp n$, $n\geq2$, be a biholomorphism and let $Λ\subseteq \mathbb{C}\sp n$ be a compact $f$-invariant set such that $f|Λ$ is partially hyperbolic. We give equivalent conditions to hyperbolicity on $Λ$. In the particular case of generalized Hénon map with dominated splitting in the Julia set $J$, we characterize the hyperbolicity of $J$.

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Francisco Valenzuela Henriquez. 2010-05-12. Equivalent conditions for hyperbolicity on partially hyperbolic holomorphic map. https://arxiv.org/abs/1005.2206

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