Julia sets on ℝℙ² and dianalytic dynamics

Goodman, Sue; Hawkins, Jane

doi:10.1090/S1088-4173-2014-00265-3

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.

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