An augmented phase plane approach for discrete planar maps: Introducing next-iterate operators

The next-iterate operators and corresponding next-iterate root-sets and root-curves associated with the nullclines of a planar discrete map are introduced. How to augment standard phase portraits that include the nullclines and the direction field, by including the signs of the root-operators associated with their nullclines, thus producing an augmented phase portrait, is described. The sign of a next-iterate operator associated with a …