Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 449-463

DYNAMICAL CONVERGENCE OF A CERTAIN POLYNOMIAL FAMILY TO f_a(z) = z + e^z + a

Shunsuke Morosawa

Kochi University, Faculty of Science, Department of Natural Science
2-5-1 Akebonocho, Kochishi, Kochi, 780-8520, Japan; morosawa 'at' kochi-u.ac.jp

Abstract. A transcendental entire function f_a(z) = z + e^z + a may have a Baker domain or a wandering domain, which never appear in the dynamics of polynomials. We consider a sequence of polynomials P_a,d(z) = (1 + a/d)z + (1 + z/d)^d+1 + a, which converges uniformly on compact sets to f_a as d → ∞. We show its dynamical convergence under a certain assumption, even though f_a has a Baker domain or a wandering domain. We also investigate the parameter spaces of f_a and P_a,d.

2010 Mathematics Subject Classification: Primary 37F10; Secondary 30D05.

Key words: Complex dynamics, transcendental entire function, Baker domain, wandering domain, Carathéodory convergence, Hausdorff convergence.

Reference to this article: S. Morosawa: Dynamical convergence of a certain polynomial family to f_a(z) = z + e^z + a. Ann. Acad. Sci. Fenn. Math. 40 (2015), 449-463.

Full document as PDF file

doi:10.5186/aasfm.2015.4028

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