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.

Source : oai:HAL:hal-01283158v1

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)

Section: Proceedings

Published on: January 1, 2012

Submitted on: January 31, 2017

Keywords: pentagram map, singularity confinement, decorated polygon,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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