The pentagram map: geometry, algebra, integrability

2012 ◽  
pp. 127-135
Author(s):  
Valentin Ovsienko
Keyword(s):  
Pentagram Map

scholarly journals $Y$ -meshes and generalized pentagram maps

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Max Glick ◽  
Pavlo Pylyavskyy
Keyword(s):  
Projective Geometry ◽  
Cluster Algebra ◽  
Cluster Theory ◽  
Rich Family ◽  
International Audience ◽  
Pentagram Map

International audience 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. Nous introduisons une famille de généralisations de l’application pentagramme. Chacune produit une configuration infinie de points et de lignes avec quatre points sur chaque ligne. Ces systèmes ont une description des $Y$ -mutations dans une algèbre amassée, un nouveau lien entre la théorie d’algèbres amassées et la géométrie projective.

scholarly journals The Limit Point of the Pentagram Map

2018 ◽  
Vol 2020 (9) ◽  
pp. 2818-2831 ◽  
Author(s):  
Max Glick
Keyword(s):  
Dynamical System ◽  
Limit Point ◽  
Convex Polygon ◽  
Discrete Dynamical System ◽  
Explicit Description ◽  
Cartesian Coordinates ◽  
The Subject ◽  
Pentagram Map

Abstract The pentagram map is a discrete dynamical system defined on the space of polygons in the plane. In the 1st paper on the subject, Schwartz proved that the pentagram map produces from each convex polygon a sequence of successively smaller polygons that converges exponentially to a point. We investigate the limit point itself, giving an explicit description of its Cartesian coordinates as roots of certain degree three polynomials.

Geometry and Dynamics of the Pentagram Map

2009 ◽  
Author(s):  
S. Tabachnikov ◽  
Piotr Kielanowski ◽  
S. Twareque Ali ◽  
Anatol Odzijewicz ◽  
Martin Schlichenmaier ◽  
...  
Keyword(s):  
Pentagram Map

scholarly journals Non-commutative integrability of the Grassmann pentagram map

2020 ◽  
Vol 373 ◽  
pp. 107309
Author(s):  
Nicholas Ovenhouse
Keyword(s):  
Pentagram Map

scholarly journals The Pentagram Map is Recurrent

2001 ◽  
Vol 10 (4) ◽  
pp. 519-528 ◽  
Author(s):  
Richard Evan Schwartz
Keyword(s):  
Pentagram Map

scholarly journals T-systems and the pentagram map

2015 ◽  
Vol 87 ◽  
pp. 233-247 ◽  
Author(s):  
Rinat Kedem ◽  
Panupong Vichitkunakorn
Keyword(s):  
Pentagram Map

scholarly journals Liouville–Arnold integrability of the pentagram map on closed polygons

2013 ◽  
Vol 162 (12) ◽  
pp. 2149-2196 ◽  
Author(s):  
Valentin Ovsienko ◽  
Richard Evan Schwartz ◽  
Serge Tabachnikov
Keyword(s):  
Pentagram Map
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