Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1892773 | Journal of Geometry and Physics | 2015 | 11 Pages |
Abstract
We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and define a universal class of pentagram maps, which are proved to possess projective duality. We show that in many cases the pentagram map cannot be included into integrable flows as a time-one map, and discuss how the corresponding notion of discrete integrability can be extended to include jumps between invariant tori. We also present a numerical evidence that certain generalizations of the integrable 2D pentagram map are non-integrable and present a conjecture for a necessary condition of their discrete integrability.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Boris Khesin, Fedor Soloviev,