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Fatou Components of Attracting Skew Products: From Polynomial Classification to Transcendental Complexity
We study the Fatou components of holomorphic skew products $F \colon \mathbb{C}^2 \to \mathbb{C}^2, F(z,w) = (f(z) + r(z,w), g(w))$ near an attracting invariant fiber, introducing a refined classification of components on the fiber: bulging, partial bulging, and nowhere bulging. For polynomial skew
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