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An elliptic Newton flow is a dynamical system that can be interpreted as acontinuous version of Newton's iteration method for finding the zeros of anelliptic function f. Previous work focusses on structurally stable flows (i.e.,the phase portraits are topologically invariant under perturbations of thepoles and zeros for f), including a classification / representation result forsuch flows in terms of Newton graphs (i.e., cellularly embedded toroidal graphsfulfilling certain combinatorial properties). The present paper deals withnon-structurally stable elliptic Newton flows determined by pseudo Newtongraphs (i.e., cellularly embedded toroidal graphs, either generated by a Newtongraph, or the so called nuclear Newton graph, exhibiting only one vertex andtwo edges). Our study results into a deeper insight in the creation ofstructurally stable Newton flows and the bifurcation of non-structurally stableNewton flows.

Newton flows for elliptic functions IV, Pseudo Newton graphs: bifurcation & creation of flows