A bouquet of pseudo-arcs
Tania Gricel Benitez, Lasse Rempe

TL;DR
This paper constructs a simpler, explicit transcendental entire function with a Julia set forming a bouquet of pseudo-arcs, advancing understanding of complex dynamics and fractal structures.
Contribution
It provides a more straightforward, explicit construction of a transcendental entire function with a Julia set composed of pseudo-arcs, improving on previous complex examples.
Findings
The constructed function has lower order 1/2.
The Julia set forms a bouquet of pseudo-arcs.
The construction simplifies previous complex examples.
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 , while the lower order in the previously known example is infinite.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Meromorphic and Entire Functions · Mathematics and Applications
