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arXiv · 1704.00544

Rational maps with Fatou components of arbitrarily large connectivity

Jordi Canela
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Abstract

We study the family of singular perturbations of Blaschke products $B_{a,λ}(z)=z^3\frac{z-a}{1-\overline{a}z}+\fracλ{z^2}$. We analyse how the connectivity of the Fatou components varies as we move continuously the parameter $λ$. We prove that all possible escaping configurations of the critical point $c_-(a,λ)$ take place within the parameter space. In particular, we prove that there are maps $B_{a,λ}$ which have Fatou components of arbitrarily large finite connectivity within their dynamical planes.

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Jordi Canela. 2017-04-03. Rational maps with Fatou components of arbitrarily large connectivity. https://arxiv.org/abs/1704.00544

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