On holomorphic partially hyperbolic systems

Disheng Xu; Jiesong Zhang

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arXiv · 2401.04310

On holomorphic partially hyperbolic systems

Disheng Xu·Jiesong Zhang

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Abstract

We construct examples illustrating that dynamically-defined distributions of holomorphic diffeomorphisms on compact complex manifolds are not necessarily holomorphic in any open subset. More precisely, for any $n\geq 5$, we construct a holomorphic fibered partially hyperbolic system on a complex $n$-fold, where the center distribution is not holomorphic in any open subset. For $n=3$ we demonstrate a contrast: the center distribution of any fibered holomorphic partially hyperbolic diffeomorphism on a complex $3$-fold is holomorphic. In particular, any such a system is a holomorphic skew product over a linear automorphism on a complex $2$-torus.

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Disheng Xu, Jiesong Zhang. 2024-01-09. On holomorphic partially hyperbolic systems. https://arxiv.org/abs/2401.04310

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