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Escape components of McMullen maps
Published online by Cambridge University Press: 28 November 2022
Abstract
We consider the McMullen maps $f_{\unicode{x3bb} }(z)=z^{n}+\unicode{x3bb} z^{-n}$ with
$\unicode{x3bb} \in \mathbb {C}^{*}$ and
$n \geq 3$. We prove that the closures of escape hyperbolic components are pairwise disjoint and the boundaries of all bounded escape components (the McMullen domain and Sierpiński holes) are quasi-circles with Hausdorff dimension strictly between
$1$ and
$2$.
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- Original Article
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- Copyright
- © The Author(s), 2022. Published by Cambridge University Press
Footnotes
The original version of this article contained an error in the name Pascale Roesch. This error has been corrected. A notice detailing this error has been published.
References
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