Dynamical convergence of a certain polynomial family to f_a(z) = z + e^z + a

Abstract

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+ 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 .

Singular values of two-parameter families λ((bz − 1)/z)μ and λ(z/(bz − 1))η

“…Usually, it is crucial to study the dynamical properties of entire or meromorphic functions if singular values exist. The importance of singular values in the dynamics of transcendental functions can be seen in [1][2][3][4]. The dynamics of one parameter family λe z , that has only one singular value, was vastly explored in [5,6].…”