Geometric Limits of Julia Sets of Maps z^n + exp(2πiθ) as n → ∞

Authors

Scott R. Kaschner, Butler UniversityFollow
Reaper Romero
David Simmons

Document Type

Article

Publication Date

2015

Publication Title

International Journal of Bifurcation and Chaos

DOI

http://dx.doi.org/10.1142/S0218127415300219

Abstract

We show that the geometric limit as n → ∞ of the Julia sets J(P_n,c) for the maps P_n,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.

Rights

Preprint of an article published in Int. J. Bifurcation Chaos 25, 1530021 (2015) [8 pages] DOI: 10.1142/S0218127415300219 © Copyright World Scientific Publishing Company

Recommended Citation

Kaschner, Scott R.; Romero, Reaper; and Simmons, David, "Geometric Limits of Julia Sets of Maps z^n + exp(2πiθ) as n → ∞" International Journal of Bifurcation and Chaos / (2015): -.
Available at https://digitalcommons.butler.edu/facsch_papers/858