Long‐diagonal pentagram maps
نویسندگان
چکیده
منابع مشابه
Y -meshes and generalized pentagram maps
We introduce a rich family of generalizations of the pentagram map sharing the property that each generates an infinite configuration of points and lines with four points on each line. These systems all have a description as Y -mutations in a cluster algebra and hence establish new connections between cluster theory and projective geometry. Résumé. Nous introduisons une famille de généralisatio...
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The pentagram map was introduced by R. Schwartz more than 20 years ago. In 2009, V. Ovsienko, R. Schwartz and S. Tabachnikov established Liouville complete integrability of this discrete dynamical system. In 2011, M. Glick interpreted the pentagram map as a sequence of cluster transformations associated with a special quiver. Using compatible Poisson structures in cluster algebras and Poisson g...
متن کاملHigher pentagram maps, weighted directed networks, and cluster dynamics
The pentagram map was introduced by R. Schwartz about 20 years ago [25]. Recently, it has attracted a considerable attention: see [11, 16, 17, 20, 21, 22, 26, 27, 28, 29, 30] for various aspects of the pentagram map and related topics. On plane polygons, the pentagram map acts by drawing the diagonals that connect second-nearest vertices and forming a new polygon whose vertices are their consec...
متن کاملPentagram Spirals
The pentagram map is a projectively natural map defined on the space of ngons. The case n = 5 is classical; it goes back at least to Clebsch in the 19th century and perhaps even to Gauss. Motzkin [Mot] also considered this case in 1945. I introduced the general version of the pentagram map in 1991. See [Sch1]. I subsequently published two additional papers, [Sch1] and [Sch2], on the topic. Now ...
متن کاملGlick’s Conjecture on the Point of Collapse of Axis-aligned Polygons under the Pentagram Maps
The pentagram map has been studied in a series of papers by Schwartz and others. Schwartz showed that an axis-aligned polygon collapses to a point under a predictable number of iterations of the pentagram map. Glick gave a different proof using cluster algebras, and conjectured that the point of collapse is always the center of mass of the axis-aligned polygon. In this paper, we answer Glick’s ...
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ژورنال
عنوان ژورنال: Bulletin of The London Mathematical Society
سال: 2023
ISSN: ['1469-2120', '0024-6093']
DOI: https://doi.org/10.1112/blms.12792