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arXiv · 1502.07901

The stable subset of a univalent self-map

Leandro Arosio
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Abstract

We give a complete description of the stable subset (the union of all backward orbit with bounded step) and of the pre-models of a univalent self-map $f: X\to X$, where $X$ is a Kobayashi hyperbolic cocompact complex manifold, such as the ball or the polydisc in $C^q$. The result is obtained studying the complex structure of a decreasing intersection of complex manifolds, all biholomorphic to $X$.

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Leandro Arosio. 2015-02-27. The stable subset of a univalent self-map. https://arxiv.org/abs/1502.07901

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