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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A dichotomy for Fatou components of polynomial skew products
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by Roland K. W. Roeder
Conform. Geom. Dyn. 15 (2011), 7-19
Published electronically: February 3, 2011


We consider polynomial maps of the form $f(z,w) = (p(z),q(z,w))$ that extend as holomorphic maps of $\mathbb {CP}^2$. Mattias Jonsson introduces in “Dynamics of polynomial skew products on $\mathbf {C}^2$” [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.
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Bibliographic Information
  • Roland K. W. Roeder
  • Affiliation: IUPUI Department of Mathematical Sciences, LD Building, Room 270, 402 North Blackford Street, Indianapolis, Indiana 46202-3267
  • MR Author ID: 718580
  • Email:
  • Received by editor(s): May 12, 2010
  • Received by editor(s) in revised form: January 1, 2011, and January 2, 2011
  • Published electronically: February 3, 2011
  • Additional Notes: Research was supported in part by startup funds from the Department of Mathematics at IUPUI
  • © Copyright 2011 Roland K. W. Roeder
  • Journal: Conform. Geom. Dyn. 15 (2011), 7-19
  • MSC (2010): Primary 32H50; Secondary 37F20, 57R19
  • DOI:
  • MathSciNet review: 2769221