APPEARANCE AND DISAPPEARANCE OF A DOVETAIL STRUCTURE IN THE PARAMETER PLANE OF AN n-DIMENSIONAL MAP

Abstract

A dovetail structure is made up of two cusp points located on a same fold bifurcation curve in a parameter plane of a discrete dynamical system defined by a differentiable map. When a third parameter varies, an existing dovetail structure may disappear by the merging of the two cusp points, or a dovetail structure may appear by the creation of two cusp points on a locally smooth fold bifurcation curve. This paper presents a method permitting to determine the value of the third parameter at which a dovetail structure may appear or disappear in n-dimensional systems. The exposed method is based on the definition of a new singular point, called E-point, belonging to a fold bifurcation curve.