Infinite entropy for transcendental entire functions with an omitted value
Anna Miriam Benini, John Erik Forn{\ae}ss, Han Peters
TL;DR
This paper proves that transcendental entire functions with an omitted value have infinite entropy, highlighting a fundamental dynamical property of such functions in complex analysis.
Contribution
It establishes that entire transcendental functions with an omitted value possess infinite entropy, a significant insight into their dynamical complexity.
Findings
Transcendental entire functions with omitted values have infinite entropy.
A proof for general transcendental entire functions will be provided in future work.
Abstract
We prove that entire transcendental holomorphic functions with an omitted value have infinite entropy. A proof for general transcendental entire functions will be given in an upcoming paper.
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Taxonomy
TopicsMeromorphic and Entire Functions · Mathematical Dynamics and Fractals · Holomorphic and Operator Theory