Abstract
This paper concerns bifurcation properties of a two-dimensional map T. Three configurations of fold and flip bifurcation curves, centered around a fold cusp point play a fundamental role. They are called the crossroad area, the spring area, and the saddle area. More than one cusp point can exist in the same fold bifurcation curve constituting, with the related bifurcation curves, a dovetail bifurcation structure. Finally, an application is given.
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