Geometry and dynamics of the pentagram map

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We survey the recent joint work with V. Ovsienko and R. Schwartz on the Pentagram Map, a projectively natural transformation of polygons. The main result is that this map is completely integrable. The Pentagram Map is a geometrically natural discretization of the Boussinesq equation, one of the most popular completely integrable PDEs. We show that the integrability mechanism that works for the Pentagram Map fails for similar projectively natural iterations.

Original languageEnglish (US)
Title of host publicationGeometric Methods in Physics - Proceedings of the XXVIII Workshop on Geometric Methods in Physics
Number of pages10
StatePublished - Dec 1 2009
Event28th Workshop on Geometric Methods in Physics, WGMP 2009 - Bialowieza, Poland
Duration: Jun 28 2009Jul 4 2009

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


Other28th Workshop on Geometric Methods in Physics, WGMP 2009

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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