Simply connected fast escaping Fatou components
D. J. Sixsmith
TL;DR
This paper constructs an example of a transcendental entire function with a simply connected fast escaping Fatou component and introduces a new criterion for identifying points in the fast escaping set.
Contribution
It provides the first example of such a function with a simply connected fast escaping Fatou component and establishes a new criterion for fast escaping points.
Findings
Existence of a transcendental entire function with a simply connected fast escaping Fatou component
No multiply connected Fatou components in the constructed example
New criterion for points to be in the fast escaping set
Abstract
We give an example of a transcendental entire function with a simply connected fast escaping Fatou component, but with no multiply connected Fatou components. We also give a new criterion for points to be in the fast escaping set.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Meromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems