Devaney, Robert L. \(e^ z\): Dynamics and bifurcations. (English) Zbl 0874.58066 Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, No. 2, 287-308 (1991). Summary: We describe some of the dynamical behavior of the complex exponential \(\lambda\exp z\). For various values of \(\lambda\), this family exhibits chaotic behavior on the entire complex plane. For other values, the dynamics are relatively tame. We show how to analyze this behavior via symbolic dynamics and investigate the structural instability at various parameter values. Finally, we describe the relationship between the parameter space for the exponential family and the related families of polynomials given by \(\lambda(1+{z\over d})^d\). Cited in 14 Documents MSC: 37F99 Dynamical systems over complex numbers 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37E99 Low-dimensional dynamical systems 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable Keywords:complex exponential; chaotic behaviour; complex plane; symbolic dynamics; structural instability; polynomials PDF BibTeX XML Cite \textit{R. L. Devaney}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, No. 2, 287--308 (1991; Zbl 0874.58066) Full Text: DOI OpenURL