Julia sets on $\mathbb {R}\mathbb {P}^2$ and dianalytic dynamics
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- by Sue Goodman and Jane Hawkins
- Conform. Geom. Dyn. 18 (2014), 85-109
- DOI: https://doi.org/10.1090/S1088-4173-2014-00265-3
- 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.References
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Bibliographic 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
- MR Author ID: 82840
- Email: jmh@math.unc.edu
- 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 - © Copyright 2014 American Mathematical Society
- Journal: Conform. Geom. Dyn. 18 (2014), 85-109
- MSC (2010): Primary 37F45, 37E99, 57M99
- DOI: https://doi.org/10.1090/S1088-4173-2014-00265-3
- MathSciNet review: 3200664