Julia sets on ℝℙ² and dianalytic dynamics

We study analytic maps of the sphere that project to well-defined maps on the nonorientable real surface R P 2 \mathbb {RP}^2 . We parametrize all maps with two critical points on the Riemann sphere C ∞ \mathbb {C}_\infty , and study the moduli space associated to these maps. These maps are also cal...

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Bibliographic Details
Published in:Conformal geometry and dynamics 2014-05, Vol.18 (6), p.85-109
Main Authors: Goodman, Sue, Hawkins, Jane
Format: Article
Language:English
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Summary:We study analytic maps of the sphere that project to well-defined maps on the nonorientable real surface R P 2 \mathbb {RP}^2 . We parametrize all maps with two critical points on the Riemann sphere C ∞ \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 R P 2 \mathbb {RP}^2 of a subset of these maps coming from bicritical analytic maps of the sphere.
ISSN:1088-4173
1088-4173
DOI:10.1090/S1088-4173-2014-00265-3