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. It is a quantity that is infinitely small so small as to be non-measurable. In the present paper, we show that Glick's operator can be interpreted as the infinitesimal monodromy of the polygon. In normal English, infinitesimal means something that is extremely small, but in mathematics it has an even stronger meaning. 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. In the present paper, we show that Glick's operator can be interpreted as the infinitesimal monodromy of the polygon. 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
0 kommentar(er)
