Namely, there exists a certain natural infinitesimal perturbation of a polygon, which is again a polygon but in general not closed what Glick's operator measures is the extent to which this perturbed polygon does not close up. In the present paper, we show that Glick's operator can be interpreted as the infinitesimal monodromy of the polygon. Furthermore, as recently proved by Glick, coordinates of that limit point can be computed as an eigenvector of a certain operator associated with the polygon. The orbit of a convex polygon under this map is a sequence of polygons that converges exponentially to a point. Namely, there exists a certain natural infinitesimal perturbation of a polygon, which is again a polygon but in general not closed what Glick's operator measures is the extent to which this perturbed polygon does not close up.ĪB - The pentagram map takes a planar polygon P to a polygon P ′ whose vertices are the intersection points of the consecutive shortest diagonals of P. This gives rise to cognitive conflictin terms of cognitive images that conflict with the formal definition. Furthermore, as recently proved by Glick, coordinates of that limit point can be computed as an eigenvector of a certain operator associated with the polygon. In the case of the limit, the process of tending to a limit is a potentialprocess that may neverreach its limit (it may not even have an explicit finite procedure to carry out the limit process). N2 - The pentagram map takes a planar polygon P to a polygon P ′ whose vertices are the intersection points of the consecutive shortest diagonals of P. T1 - The Limit Point of the Pentagram Map and Infinitesimal Monodromy
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