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Conformal Geometry and Dynamics

ISSN 1088-4173



On the classification of critically fixed rational maps

Authors: Kristin Cordwell, Selina Gilbertson, Nicholas Nuechterlein, Kevin M. Pilgrim and Samantha Pinella
Journal: Conform. Geom. Dyn. 19 (2015), 51-94
MSC (2010): Primary 37F20; Secondary 05C10, 57M12, 57M15, 20E08
Published electronically: March 19, 2015
MathSciNet review: 3323420
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Abstract: We discuss the dynamical, topological, and algebraic classification of rational maps $ f: \widehat {\mathbb{C}} \to \widehat {\mathbb{C}}$, each of whose critical points $ c$ is also a fixed-point of $ f$, i.e., $ f(c)=c$.

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Additional Information

Kristin Cordwell
Affiliation: 360 W. 43rd St, Apt. S8E, New York, New York 10036

Selina Gilbertson
Affiliation: Department of Mathematics and Statistics, P.O. Box 5717, Northern Arizona University, Flagstaff, Arizona 86011

Nicholas Nuechterlein
Affiliation: 711 Catherine St., Ann Arbor, Michigan 48104

Kevin M. Pilgrim
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405

Samantha Pinella
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043

Received by editor(s): September 12, 2013
Published electronically: March 19, 2015
Article copyright: © Copyright 2015 American Mathematical Society