Dynamical Systems seminar - An atlas of wandering domains for a family of transcendental Newton maps

Speaker: Roberto Florido Llinas (Universitat de Barcelona)

Abstract: Meromorphic maps naturally arise from Newton’s root-finding method applied to an entire function F. In the transcendental case, Newton’s method may particularly fail to converge to the roots of F if the initial condition lies in a Baker or wandering domain.
In this talk, we present the simplest one-parameter family of transcendental entire functions with zeros, whose Newton’s method yields wandering domains for an open set of parameters by means of the logarithmic lifting method for periodic Fatou components. This is joint work with N. Fagella.