to $1$, the spiral approaches the initial polygon, while its center approaches the limit point of the pentagram map, see Figure \[Fig:scaling\].

We note that the scaling symmetry is actually only defined on projective equivalence classes of polygons as opposed to actual polygons. This makes the family of polygons $P_z$ we used to define the infinitesimal monodromy non-unique. After reviewing basic notions in Section \[Sec:back\], we show in Section \[Sec:im\] that the infinitesimal monodromy does not depend on the family used to define it. The proof of Theorem \[thm1\] is given in Section \[Sec:proof\].

We end the introduction by mentioning a possible future direction. The notion of infinitesimal monodromy is well-defined for polygons in any dimension and any scaling operation. For multidimensional polygons, there are different possible scalings, corresponding to different integrable generalizations of the pentagram map [@khesin2013; @khesin2016]. It would be interesting to investigate the infinitesimal monodromy in those cases, along with its possible relation to the limit point of the corresponding pentagram maps. As for now, it is not even known if such a limit point exists for any class of multidimensional polygons satisfying a convexity-type condition.

It also seems that the infinitesimal monodromy in ${\mathbb P}^1$ is 