We study the dynamics of a family of polynomial functions and the relationship to the dynamics of a related entire transcendental family of functions. As the degree of the polynomial approaches infinity, the polynomial functions converge uniformly on compact sets to a function that is a product of a power map and the exponential function. The advantage to the approach in the paper is that we can use the relatively simple, although high degree, polynomial functions to aid our understanding of the dynamics of the related transcendental entire function. We study properties both in the dynamical plane as well as in the parameter plane.

Becker, Devin, Joanna Furno, and Lorelei Koss. Dynamical Convergence of Polynomials to Products of Power Maps and the Exponential. New York Journal of Mathematics 29 (2023): 441-466. https://nyjm.albany.edu/j/2023/29-19.html

© 2023. The Author(s)
This is an Open Access article published in the Open Access journal New York Journal of Mathematics. This publication is made available under the Creative Commons Attribution 4.0 International License (CC BY 4.0) : https://creativecommons.org/licenses/by/4.0/

Lorelei Koss is a professor of Mathematics at Dickinson College.

This published version is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit New York Journal of Mathematic's (NYJM) Website. https://nyjm.albany.edu/j/2023/29-19.html