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

 

Julia sets on $ \mathbb{R}\mathbb{P}^2$ and dianalytic dynamics


Authors: Sue Goodman and Jane Hawkins
Journal: Conform. Geom. Dyn. 18 (2014), 85-109
MSC (2010): Primary 37F45, 37E99, 57M99
Published electronically: May 7, 2014
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Abstract: We study analytic maps of the sphere that project to well-defined maps on the nonorientable real surface $ \mathbb{RP}^2$. We parametrize all maps with two critical points on the Riemann sphere $ \mathbb{C}_\infty $, and study the moduli space associated to these maps. These maps are also called quasi-real maps and are characterized by being conformally conjugate to a complex conjugate version of themselves. We study dynamics and Julia sets on $ \mathbb{RP}^2$ of a subset of these maps coming from bicritical analytic maps of the sphere.


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Additional Information

Sue Goodman
Affiliation: Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250, Chapel Hill, North Carolina 27599-3250
Email: seg@email.unc.edu

Jane Hawkins
Affiliation: Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250, Chapel Hill, North Carolina 27599-3250
Address at time of publication: National Science Foundation, 4201 Wilson Blvd., Arlington, Virginia 22230
Email: jmh@math.unc.edu

DOI: http://dx.doi.org/10.1090/S1088-4173-2014-00265-3
PII: S 1088-4173(2014)00265-3
Keywords: Complex dynamics, Julia sets, dianalytic mappings, real projective plane
Received by editor(s): July 10, 2013
Received by editor(s) in revised form: January 5, 2014, and February 5, 2014
Published electronically: May 7, 2014
Additional Notes: This work was completed while the second author was working at and supported by the National Science Foundation
Any opinion, findings, and conclusions expressed in this paper are those of the author(s) and do not necessarily reflect the views of the National Science Foundation
Article copyright: © Copyright 2014 American Mathematical Society