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.
Publié le : 1997-05-14
Classification:
iteration,
uniform convergence,
entire functions,
Julia set,
Fatou set,
hyperbolic components,
multicorns,
30D05,
54H20,
58F23
@article{1047649999,
author = {Krauskopf, Bernd and Kriete, Hartje},
title = {Hausdorff convergence and the limit shape of the unicorns},
journal = {Experiment. Math.},
volume = {6},
number = {4},
year = {1997},
pages = { 117-135},
language = {en},
url = {http://dml.mathdoc.fr/item/1047649999}
}
Krauskopf, Bernd; Kriete, Hartje. Hausdorff convergence and the limit shape of the unicorns. Experiment. Math., Tome 6 (1997) no. 4, pp. 117-135. http://gdmltest.u-ga.fr/item/1047649999/