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arXiv · 2010.09845

Criniferous entire maps with absorbing Cantor bouquets

Leticia Pardo-Simón
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Abstract

It is known that, for many transcendental entire functions in the Eremenko-Lyubich class $\mathcal{B}$, every escaping point can eventually be connected to infinity by a curve of escaping points. When this is the case, we say that the functions are criniferous. In this paper, we extend this result to a new class of maps in $\mathcal{B}$. Furthermore, we show that if a map belongs to this class, then its Julia set contains a Cantor bouquet; in other words, it is a subset of $\mathbb{C}$ ambiently homeomorphic to a straight brush.

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Leticia Pardo-Simón. 2020-10-19. Criniferous entire maps with absorbing Cantor bouquets. https://arxiv.org/abs/2010.09845

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