Pentagram map

In mathematics, the pentagram map is a discrete dynamical system acting on polygons in the projective plane. It defines a new polygon by taking the intersections of the "shortest" diagonals, and constructs a new polygon from these intersections. This is a projectively equivariant procedure, hence it descends to the moduli space of polygons and defines another dynamical system (which is also referred to as the pentagram map). It was first introduced by Richard Schwartz in 1992.

The pentagram map on the moduli space is famous for its complete integrability and its interpretation as a cluster algebra.

It admits many generalizations in projective spaces and other settings.

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