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 http://www.umr.edu/~pilgrim/Research/Census/WebPages/Main/Main.html
ahmadi:thesis Davood Ahmadi, Dynamics of certain rational maps of degree two, Ph.D. thesis, University of Liverpool, 1991.
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- Eva Brezin
- Affiliation: 993 Amsterdam Ave., Apt. 4a, New York, NY 10025
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- Rosemary Byrne
- Affiliation: Apt. 800, 1301 Massachusetts Ave. NW, Washington, DC 20005
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- Joshua Levy
- Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720
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- Kevin Pilgrim
- Affiliation: Department of Mathematics and Statistics, University of Missouri at Rolla, Rolla, MO 65409-0020
- MR Author ID: 614176
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- Kelly Plummer
- Affiliation: Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138
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- 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
- © Copyright 2000 American Mathematical Society
- Journal: Conform. Geom. Dyn. 4 (2000), 35-74
- MSC (2000): Primary 37F10; Secondary 13P10
- DOI: https://doi.org/10.1090/S1088-4173-00-00050-3
- MathSciNet review: 1749249