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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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.


Proof of a folklore Julia set connectedness theorem and connections with elliptic functions
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by Jane M. Hawkins PDF
Conform. Geom. Dyn. 17 (2013), 26-38 Request permission


We prove the following theorem about Julia sets of the maps \[ f_{n,p,\gamma }(z)= z^n + \frac {\gamma }{z^p}, \] for integers $n,p \geq 2$, $\gamma \in \mathbb {C}$ by using techniques developed for the Weierstrass elliptic $\wp$ function and adapted to this setting.

Folklore connectedness theorem: If $f_{n,p,\gamma }$ has a bounded critical orbit, then $J(f_{n,p,\gamma })$ is connected.

This is related to connectivity results by the author and others about $J(\wp )$, where $\wp$ denotes the Weierstrass elliptic $\wp$ function, especially where the period lattice has some symmetry. We illustrate several further connections between the dynamics of some specific elliptic functions and the family $f_{n,p,\gamma }$ for some values of $n$ and $p$.

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Additional Information
  • Jane M. Hawkins
  • Affiliation: Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250, Chapel Hill, North Carolina 27599-3250
  • MR Author ID: 82840
  • Email:
  • Received by editor(s): July 15, 2012
  • Published electronically: February 14, 2013
  • Additional Notes: This work was partially funded by a University of North Carolina, University Research Council Grant
  • © Copyright 2013 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 17 (2013), 26-38
  • MSC (2010): Primary 37F10, 37F45; Secondary 30D05, 30B99
  • DOI:
  • MathSciNet review: 3019711