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- W2800934282 abstract "We consider polynomial maps of the form f(z,w) = (p(z),q(z,w)) that extend as holomorphic maps of CP^2. Mattias Jonsson introduces in (Math. Ann., 1999) a notion of connectedness for such polynomial skew products that is analogous to connectivity for the Julia set of a polynomial map in one-variable. We prove the following dichotomy: if f is an Axiom-A polynomial skew product, and f is connected, then every Fatou component of f is homeomorphic to an open ball; otherwise, some Fatou component of f has infinitely generated first homology." @default.
- W2800934282 created "2018-05-17" @default.
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- W2800934282 date "2010-05-13" @default.
- W2800934282 modified "2023-09-27" @default.
- W2800934282 title "A fundamental dichotomy for Fatou components of polynomial skew products" @default.
- W2800934282 hasPublicationYear "2010" @default.
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