Pentagram map

In mathematics, the pentagram map is a discrete dynamical system acting on polygons in the projective plane. It defines a new polygon whose vertices are obtained as the intersection points of the shortest diagonals of the initial polygon. 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 link with cluster algebras.

It admits many generalizations in projective spaces and other settings.

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