Geodesic
On singularity confinement for the pentagram map
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 3, pp. 597-635.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The pentagram map, introduced by R. Schwartz, is a birational map on the configuration space of polygons in the projective plane. We study the singularities of the iterates of the pentagram map. We show that a "typical" singularity disappears after a finite number of iterations, a confinement phenomenon first discovered by Schwartz. We provide a method to bypass such a singular patch by directly constructing the first subsequent iterate that is well-defined on the singular locus under consideration. The key ingredient of this construction is the notion of a decorated (twisted) polygon, and the extension of the pentagram map to the corresponding decorated configuration space.
Keywords: pentagram map, singularity confinement, alternating sign matrix, decorated polygon 
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     author = {Glick, Max},
     title = {On singularity confinement for the pentagram map},
     journal = {Journal of Algebraic Combinatorics},
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     number = {3},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__38_3_a5/}
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Glick, Max. On singularity confinement for the pentagram map. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 3, pp. 597-635. http://geodesic.mathdoc.fr/item/JAC_2013__38_3_a5/