Higher pentagram maps, weighted directed networks, and cluster dynamics

Michael Gekhtman, Michael Shapiro, Serge Tabachnikov, Alek Vainshtein

Research output: Contribution to journalArticlepeer-review


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 languageAmerican English
Pages (from-to)1-17
Number of pages17
JournalElectronic Research Announcements in Mathematical Sciences
StatePublished - 2012


  • Cluster dynamics
  • Discrete integrable system
  • Pentagram map

All Science Journal Classification (ASJC) codes

  • General Mathematics


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