The doodle of a finitely determined map germ from R2 to R3

Let f : U subset of R-2 -> R-3 be a representative of a finitely determined map germ f : (R-2, 0) -> (R-3, 0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere s(epsilon)(2) centered at the origin in R-3, call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles. (C) 2009 Elsevier Inc. All rights reserved.