The pentagram map
Schwartz, Richard
Experiment. Math., Tome 1 (1992) no. 4, p. 71-81 / Harvested from Project Euclid
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We consider the pentagram map on the space of plane convex pentagons obtained by drawing a pentagon's diagonals, recovering unpublished results of Conway and proving new ones. We generalize this to a "pentagram map'' on convex polygons of more than five sides, showing that iterated images of any initial polygon converge exponentially fast to a point. We conjecture that the asymptotic behavior of this convergence is the same as under a projective transformation. Finally, we show a connection between the pentagram map and a certain flow defined on parametrized curves.
Publié le : 1992-05-14
Classification:  52A10 
@article{1048709118,
     author = {Schwartz, Richard},
     title = {The pentagram map},
     journal = {Experiment. Math.},
     volume = {1},
     number = {4},
     year = {1992},
     pages = { 71-81},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1048709118}
}

Schwartz, Richard. The pentagram map. Experiment. Math., Tome 1 (1992) no. 4, pp.  71-81. http://gdmltest.u-ga.fr/item/1048709118/