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arXiv · 2105.10391

A bouquet of pseudo-arcs

Tania Gricel Benitez·Lasse Rempe
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Abstract

We prove the existence of a transcendental entire function whose Julia set is a "bouquet of pseudo-arcs". More precisely, the union of the Julia set with infinity is an uncountable union of pseudo-arcs, which are pairwise disjoint except at infinity. The existence of such a function follows from a more general result of the second author, but our construction is considerably simpler and more explicit. In particular, the function we construct can be chosen to have lower order $1/2$, while the lower order in the previously known example is infinite.

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Tania Gricel Benitez, Lasse Rempe. 2021-05-21. A bouquet of pseudo-arcs. https://arxiv.org/abs/2105.10391

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