Valley floor gradient extremal

A gradient extremal (GE) of the Miiller-Brown potential (see Figure 15 [28]) is a suitable example showing how the definition of these curves works The bowl of Mini is a deep, long, and relatively straight valley. The col of SPi opens to this main valley and a steepest descent path goes downhill perpendicular to the contour lines of the floor. At the valley floor, it joins in the floor line. However, we cannot decide at which point the lines cross, because this is an asymptotic junction. 

The uphill stream bed path (minimum gradient extremal, dotted line in the l.h.s.) complicated path tracing, e.g. due to dissipation of the original valley floor. 

Foremost, we have to remark that a steepest descent path is in general not identical with a valley floor at all, even if it is coming from a saddle point (see Sect. 3.3). This is due to the fact that a valley floor has to be described by a gradient extremal curve which can have a direction other than the gradient itself (see Sect. 3.2, Example 3, and Examples 4-6 with valleys which flatten out somewhere at the slope). In Fig.18 we give a view of such a drastic case. 

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