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Quadratic rational maps lacking period 2 orbits
Author(s):
Rika
Hagihara
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3077-3090.
MSC (2000):
Primary 37F45;
Secondary 30D05, 37F10
Posted:
March 18, 2009
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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:
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
Posted:
March 18, 2009
Communicated by:
Jane M. Hawkins
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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