Florido Llinàs, RobertFagella Rabionet, Núria2025-07-292025-07-292024-11-250308-2105https://hdl.handle.net/2445/222644We present a one-parameter family $F_\lambda$ of transcendental entire functions with zeros, whose Newton's method yields wandering domains, coexisting with the basins of the roots of $F_\lambda$. Wandering domains for Newton maps of zero-free functions have been built before by, e.g. Buff and Rückert [23] based on the lifting method. This procedure is suited to our Newton maps as members of the class of projectable functions (or maps of the cylinder), i.e. transcendental meromorphic functions $f(z)$ in the complex plane that are semiconjugate, via the exponential, to some map $g(w)$, which may have at most a countable number of essential singularities. In this paper, we make a systematic study of the general relation (dynamical and otherwise) between $f$ and $g$, and inspect the extension of the logarithmic lifting method of periodic Fatou components to our context, especially for those $g$ of finite-type. We apply these results to characterize the entire functions with zeros whose Newton's method projects to some map $g$ which is defined at both 0 and $\infty$. The family $F_\lambda$ is the simplest in this class, and its parameter space shows open sets of $\lambda$-values in which the Newton map exhibits wandering or Baker domains, in both cases regions of initial conditions where Newton's root-finding method fails.50 p.application/pdfengcc by (c) Robert Florido et al., 2024http://creativecommons.org/licenses/by/3.0/es/Sistemes dinàmics complexosFuncions meromorfesComplex dynamical systemsMeromorphic functionsinfo:eu-repo/semantics/article7538262025-07-29info:eu-repo/semantics/openAccess