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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

Mapping schemes realizable by obstructed topological polynomials


Author: Gregory A. Kelsey
Journal: Conform. Geom. Dyn. 16 (2012), 44-80
MSC (2010): Primary 37F20; Secondary 20F65
Published electronically: March 13, 2012
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Abstract: In 1985, Levy used a theorem of Berstein to prove that all hyperbolic topological polynomials are equivalent to complex polynomials. We prove a partial converse to the Berstein-Levy Theorem: given post-critical dynamics that are in a sense strongly non-hyperbolic, we prove the existence of topological polynomials which are not equivalent to any complex polynomial that realize these post-critical dynamics. This proof employs the theory of self-similar groups to demonstrate that a topological polynomial admits an obstruction and produces a wealth of examples of obstructed topological polynomials.


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Additional Information

Gregory A. Kelsey
Affiliation: Department of Mathematics, Computing Sciences, and Physics, Immaculata University, P.O. Box 648, Immaculata, Pennsylvania 19345
Email: gkelsey@immaculata.edu

DOI: http://dx.doi.org/10.1090/S1088-4173-2012-00239-1
PII: S 1088-4173(2012)00239-1
Keywords: Combinatorics of complex dynamics, self-similar groups
Received by editor(s): January 27, 2011
Received by editor(s) in revised form: July 26, 2011
Published electronically: March 13, 2012
Additional Notes: The author acknowledges support from National Science Foundation grant DMS 08-38434 “EMSW21-MCTP: Research Experience for Graduate Students”.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.