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Local connectedness of the Julia set of the family $z^m(z^n-b)$
Published online by Cambridge University Press: 01 April 1998
Abstract
We study the local connectedness of the Julia set of the family $f_b(z)=z^m(z^n-b)$. Assuming that the Julia set is connected and depending on whether $m=1$ or $m>1$, a sufficient condition for the local connectivity of the Julia set is obtained. This complements the known results of Yoccoz–Hubbard–Branner for $m=n=1$.
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- Research Article
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- 1998 Cambridge University Press
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