We discuss connectivity properties of Julia sets of the parameterized Dixon elliptic functions. Our main result is that the connectivity locus of the parameterized Dixon sine function is the exterior of the open unit disc, and the Julia set is Cantor in the open unit disc minus the origin. We prove the parameterized Dixon cosine function also exhibits a fundamental dichotomy in the connectivity of the Julia set. The Julia and Fatou sets exhibit a variety of rotational symmetries, and no Herman rings exist for any function in either family.

Koss, Lorelei, and Alex Nash. Cantor and Connected Julia Sets of the Parameterized Dixon Elliptic Functions. Journal of Difference Equations and Applications 29, no. 3 (2023): 297-314. https://www.tandfonline.com/doi/full/10.1080/10236198.2023.2196360

Lorelei Koss is a professor of Mathematics at Dickinson College.

For more information on the published version, visit Taylor and Francis's Website. https://www.tandfonline.com/doi/full/10.1080/10236198.2023.2196360

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