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1997 Hausdorff convergence and the limit shape of the unicorns
Bernd Krauskopf, Hartje Kriete
Experiment. Math. 6(2): 117-135 (1997).


We discuss the Hausdorff convergence of hyperbolic components in parameter space as a one-parameter family of transcendental functions is dynamically approximated by polynomials. This convergence is strongly suggested by computer experiments and is proved in a weaker form, which is illustrated with exponential, sine and cosine families. Furthermore, we consider the convergence of subhyperbolic components. Our result also applies to the antiholomorphic exponentials, which allows us to investigate the limit shape of the unicorns.


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Bernd Krauskopf. Hartje Kriete. "Hausdorff convergence and the limit shape of the unicorns." Experiment. Math. 6 (2) 117 - 135, 1997.


Published: 1997
First available in Project Euclid: 14 March 2003

zbMATH: 0885.30023
MathSciNet: MR1474573

Primary: 30D05
Secondary: 54H20‎ , 58F23

Keywords: entire functions , Fatou set , hyperbolic components , iteration , Julia set , multicorns , Uniform convergence

Rights: Copyright © 1997 A K Peters, Ltd.

Vol.6 • No. 2 • 1997
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