A Dichotomy for Fatou Components of Polynomial Skew Products
نویسندگان
چکیده
We consider polynomial maps of the form f(z,w) = (p(z), q(z,w)) that extend as holomorphic maps of CP. Mattias Jonsson introduces in “Dynamics of polynomial skew products on C2” [Math. Ann., 314(3): 403– 447, 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.
منابع مشابه
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