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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.


Totally ramified rational maps
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by Weiwei Cui and Jun Hu
Conform. Geom. Dyn. 26 (2022), 208-234
Published electronically: December 6, 2022


Totally ramified rational maps and regularly ramified rational maps are defined and studied in this paper. We first give a complete classification of regularly ramified rational maps and show that our definition of a regularly ramified rational map is equivalent to a much stronger definition of a map of this kind given by Milnor [Dynamics in one complex variable, Princeton University Press, Princeton, NJ, 2006]. Then we show that (1) any totally ramified rational map of degree $d\leq 6$ must be regularly ramified; (2) for any integer $d>6$, there exists a totally ramified rational map of degree $d$ which is not regularly ramified. Furthermore, we count totally ramified rational maps up to degree $10$. Finally, we present explicit formulas for all totally but not regularly ramified rational maps of degree $7$ or $8$, up to pre- and post-composition by Möbius transformations.
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Bibliographic Information
  • Weiwei Cui
  • Affiliation: Shanghai Center for Mathematical Sciences, Fudan University, 2005 Songhu Road, Shanghai 200438, People’s Republic of China; and Centre for Mathematical Sciences, Lund University, Box 118, 22 100 Lund, Sweden
  • MR Author ID: 1014684
  • ORCID: 0000-0003-2505-4710
  • Email:,
  • Jun Hu
  • Affiliation: Department of Mathematics, Brooklyn College of CUNY, Brooklyn, New York 11210; Ph.D. Program in Mathematics, Graduate Center of CUNY, 365 Fifth Avenue, New York, New York 10016; and NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, People’s Republic of China
  • MR Author ID: 617732
  • ORCID: 0000-0003-4338-2048
  • Email:,
  • Received by editor(s): December 30, 2021
  • Received by editor(s) in revised form: August 28, 2022
  • Published electronically: December 6, 2022
  • Additional Notes: The work of the first author was partially supported by China Postdoctoral Science Foundation (No. 2019M651329). The work of the second author was supported by a CUNY research fellowship leave and a visiting professorship at NYUShanghai in Spring 2019.
    The second author is the corresponding author.
  • © Copyright 2022 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 26 (2022), 208-234
  • MSC (2020): Primary 37F20; Secondary 37F10
  • DOI:
  • MathSciNet review: 4518758