A dichotomy for Fatou components of polynomial skew products

, 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 connected, then every Fatou component of f has infinitely generated first homology.

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Bibliographic Details
Published in:Conformal geometry and dynamics 2011-03, Vol.15 (2), p.7-19
Main Author: Roeder, Roland
Format: Article
Language:English
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Summary:, 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 connected, then every Fatou component of f has infinitely generated first homology.
ISSN:1088-4173
1088-4173
DOI:10.1090/S1088-4173-2011-00223-2