Skip to Main Content

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.


Proof of a folklore Julia set connectedness theorem and connections with elliptic functions
HTML articles powered by AMS MathViewer

by Jane M. Hawkins
Conform. Geom. Dyn. 17 (2013), 26-38
Published electronically: February 14, 2013


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 $p$.

Similar Articles
  • Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 37F10, 37F45, 30D05, 30B99
  • Retrieve articles in all journals with MSC (2010): 37F10, 37F45, 30D05, 30B99
Bibliographic 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