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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quadratic rational maps lacking period 2 orbits


Author: Rika Hagihara
Journal: Proc. Amer. Math. Soc. 137 (2009), 3077-3090
MSC (2000): Primary 37F45; Secondary 30D05, 37F10
Published electronically: March 18, 2009
MathSciNet review: 2506466
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Abstract: We study dynamical properties of a parameterized family of quadratic rational maps, all of whose members lack period 2 orbits. We classify regions in the parameter space of the family according to the behavior of marked critical points. We characterize the parameter space by comparing it with the Mandelbrot set.


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Additional Information

Rika Hagihara
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Email: r.hagihara@unsw.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09852-9
PII: S 0002-9939(09)09852-9
Keywords: Complex dynamics, parabolic, critical points
Received by editor(s): October 23, 2008
Received by editor(s) in revised form: December 8, 2008
Published electronically: March 18, 2009
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.