On pleated singular points of first order implicit differential   equations
  We study phase portraits of a first order implicit differential equation in a neighborhood of its pleated singular point that is a non-degenerate singular point of the lifted field. Although there is no a visible local classification of implicit differential equations at pleated singular points (even in the topological category), we show that there exist only six essentially different phase portraits, which are presented. 
R. A. Chertovskih, A. O. Remizov
math.CA