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Article
Geometric Limits of Julia Sets of Maps z^n + exp(2πiθ) as n → ∞
International Journal of Bifurcation and Chaos
  • Scott R. Kaschner, Butler University
  • Reaper Romero
  • David Simmons
Document Type
Article
Publication Date
1-1-2015
Disciplines
DOI
http://dx.doi.org/10.1142/S0218127415300219
Abstract
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.
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
Citation Information
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/