We will prove this by constructing a polygonal line with no contact with the flow of the differential equation.
The polygonal line will join the origin to one of the saddle-nodes as in Figure 4.
We explain the construction of the polygonal line when 0 < [s.sub.1] [less than or equal to] 1, [s.sub.2] > 1 and [p.sub.2] < 0.
As an example of the construction of the polygonal line in the proof of Theorem 1 we present a particular case, done with Maple.
The polygonal line [GAMMA] is determined by 10 points regularly spaced on the circle of center 0 and radius 1.3.
When the matrix A is real and, assuming that the polygonal line [GAMMA] is symmetric with respect to the real axis and intersects it only in two points, half of the computation can be saved since
In this paper, we have developed a reliable method for counting the eigenvalues in a region surrounded by a user-defined polygonal line. The main difficulty to tackle lies in the step control which must be used during the complex integration along the line.
The whole polygonal line can be approximated in that way, except the 1st and the last point.
For the purpose of the problem, a polygonal line whose vertices are equidistant has to be generated.
The polygonal line
that defines the outline analytically and successively over crossed with a right line.
The program reads a sequence of points, displays them, computes their upper hull, and displays the upper hull as a polygonal line
. Again only a few explanations are needed.
The Frechet distance between two polygonal lines
is the minimum threshold e satisfying [[delta].sub.F](P, Q) [less than or equal to] [epsilon] and [epsilon] [greater than or equal to] 0, and it is generally computed using the free space of the polygonal lines