The pentagram map was extensively studied in a series of papers by V. Ovsienko, R. Schwartz and S. Tabachnikov. It was recently interpreted by M. Glick as a sequence of cluster transformations associated with a special quiver. Using compatible Poisson structures in cluster algebras and Poisson geometry of directed networks on surfaces, we generalize Glick's construction to include the pentagram map into a family of geometrically meaningful discrete integrable maps.
|Original language||English (US)|
|Number of pages||17|
|Journal||Electronic Research Announcements in Mathematical Sciences|
|State||Published - 2012|
All Science Journal Classification (ASJC) codes