The Topology of Regular Curve Families with Multiple Saddle Points
William M. Boothby · American Journal of Mathematics · 1951
Introduction. It is known that the level curves of any function f (x, y) which is harmonic in a simply connected domain form a curve family which is regular (locally homeomorphic to parallel lines) in the neighborhood of every point of the domain with the exception at most of a set of isolated points at each of which the curve family has a singularity of the multiple saddle point type (Figure 1). The central task of this and a later paper 2 iS to