We show that the geometric limit as n → ∞ of the Julia sets J(Pn,c) for the maps Pn,c(z) = zn + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.
Preprint of an article published in Int. J. Bifurcation Chaos
25, 1530021 (2015) [8 pages] DOI: 10.1142/S0218127415300219 © Copyright World Scientific Publishing Company
Scott R. Kaschner, Reaper Romero and David Simmons. "Geometric Limits of Julia Sets of Maps z^n + exp(2πiθ) as n → ∞" International Journal of Bifurcation and Chaos
Vol. 25 Iss. 8 (2015)
Available at: http://works.bepress.com/scott-kaschner/1/