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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

MARYAM RABII
MARYAM RABII
Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran (e-mail: rabiikal@math.sharif.ac.ir). Department of Mathematics, Az-Zahra University, Tehran, Iran (e-mail: shahshah@ipm.ac.ir)
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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 $m=n=1$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 2 , April 1998 , pp. 457 - 470
Copyright
1998 Cambridge University Press

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