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arXiv · 2211.15169

Uniform non-autonomous basins of attraction

Sayani Bera·Kaushal Verma
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Abstract

It has been conjectured that every stable manifold arising from a holomorphic automorphism, that acts hyperbolically on a compact invariant set, is biholomorphic to complex Euclidean space. Such stable manifolds are known to be biholomorphic to the basin of a uniformly attracting family of holomorphic maps. It is shown that the basin of a uniformly attracting family of holomorphic maps is biholomorphic to complex Euclidean space and this resolves the conjecture on the biholomorphism type of such stable manifolds affirmatively.

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Sayani Bera, Kaushal Verma. 2022-11-28. Uniform non-autonomous basins of attraction. https://arxiv.org/abs/2211.15169

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