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Conformal Geometry and Dynamics

ISSN 1088-4173



A census of rational maps

Authors: Eva Brezin, Rosemary Byrne, Joshua Levy, Kevin Pilgrim and Kelly Plummer
Journal: Conform. Geom. Dyn. 4 (2000), 35-74
MSC (2000): Primary 37F10; Secondary 13P10
Published electronically: April 4, 2000
MathSciNet review: 1749249
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Abstract: We discuss the general combinatorial, topological, algebraic, and dynamical issues underlying the enumeration of postcritically finite rational functions, regarded as holomorphic dynamical systems on the Riemann sphere. We present findings from our creation of a census of all degree two and three hyperbolic nonpolynomial maps with four or fewer postcritical points. Our data is tabulated in detail at

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Additional Information

Eva Brezin
Affiliation: 993 Amsterdam Ave., Apt. 4a, New York, NY 10025

Rosemary Byrne
Affiliation: Apt. 800, 1301 Massachusetts Ave. NW, Washington, DC 20005

Joshua Levy
Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720

Kevin Pilgrim
Affiliation: Department of Mathematics and Statistics, University of Missouri at Rolla, Rolla, MO 65409-0020
MR Author ID: 614176

Kelly Plummer
Affiliation: Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138

Keywords: Complex dynamical systems, Gröbner bases
Received by editor(s): June 16, 1999
Received by editor(s) in revised form: January 25, 2000
Published electronically: April 4, 2000
Additional Notes: Research supported in part by the National Science Foundation’s Research Experiences for Undergraduates program.
The fourth author’s research was partially supported by the NSF’s REU program at Cornell, and by NSF Grants DMS-9703724 and DMS-9996070
Article copyright: © Copyright 2000 American Mathematical Society