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...
Published as:Koss, Lorelei. Cantor Julia Sets in a Family of Even Elliptic Functions. Journal of Difference Equations and Applications 16, no. 5-6 (2010): 675-88. For more information on the published version, visit Taylor...
Published as:Goldsmith, Jeff and Lorelei Koss. Dynamical Properties of the Derivative of the Weierstrass Elliptic Function. Involve 2, no. 3 (2009): 267-88.For more information on the published version, visit Mathematical...
For more information on the published version, visit Mathematical Sciences Publisher's Website., In this paper, we investigate the dynamics of iterating the Weierstrass elliptic functions on vertical real rhombic lattices. The...
Published as:Hawkins, Jane, Lorelei Koss, and Janina Kotus. Elliptic Functions with Critical Orbits Approaching Infinity. Journal of Difference Equations and Applications, 16, no. 5-6 (2010): 613-30.For more information on...
In this paper, we investigate elliptic functions of the form , where is the Weierstrass elliptic function on a real rhombic lattice. We show that a typical function in this family has a superattracting fixed point at the origin...
We discuss properties of the Julia and Fatou sets of Weierstrass elliptic p functions arising from real lattices. We give sufficient conditions for the Julia sets to be the whole sphere and for the maps to be ergodic, exact,...
This published version is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit New York Journal of Mathematics's Website., Koss, Lorelei. "Examples of...
Clemons, Joshua J., and Lorelei Koss. Higher Order Elliptic Functions with Connected Julia Sets. Topology Proceedings 53 (2019): 57-72. (Article published online May 7, 2018)....
We analyze the existence and types of unbounded Fatou components for elliptic functions and other meromorphic functions with doubly periodic Julia sets. We show that apart from Herman rings and Siegel disks, all types of...
