2019-06-182019-06-182012-09Bernal González, L., Bonilla Ramírez, A.L. y Costakis, G. (2012). On the growth of zero-free MacLane-universal entire functions. Indagationes Mathematicae, 23 (3), 311-317.0019-3577https://hdl.handle.net/11441/87491We show that exponential growth is the critical discrete rate of growth for zero-free entire functions which are universal in the sense of MacLane. Specifically, it is proved that if the lower exponential growth order of a zero-free entire function f is finite, then f cannot be hypercyclic for the derivative operator; and, if a positive function ϕ having infinite exponential growth is fixed, then there exist zero-free hypercyclic functions which are controlled by ϕ along a sequence of radii tending to infinity.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Universal functionsD-hypercyclicityZerofree functionsExponential growth of entire functionsFinal setinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1016/j.indag.2011.12.003