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Pentagram map

In mathematics, the pentagram map is a discrete dynamical system acting on polygons in the projective plane. It defines a new polygon whose vertices are obtained as the intersection points of the shortest diagonals of the initial polygon. This is a projectively equivariant procedure, hence it descends to the moduli space of polygons and defines another…

Works, Works cited & Complete integrability

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Overview

Introduction

Definitions and first properties

Collapsing of convex polygons

Periodic orbits on the moduli space

Coordinates for the moduli space

Formulas on the moduli space

Invariant structures

Complete integrability

Connections to other topics

Generalizations

Works cited

Advanced semantic analysis

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Map overview Semantic statistics

Pentagram map

Nodes199
Edges198
Triples353
Avg. degree1.99
Density0.01005
Components1

How this topic connects Entity context

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Pentagram map

Top relations

related to Works cited · 225
Pentagram map → Abigayle, Aboud, Advanced Courses, Advances, Affolter, AGD Flows, Alek, Alexander, Alexandru, Alexey, Alfred, Algebraic Combinatorics, American Mathematical Society, Andrey, Annales, Anton, Applications, Applicazioni, ArizonaFelipe, ARMJ
related to Algebro-geometric integrability · 13
Pentagram map → Abel, Abelian, Bloch, Floquet, In, Jacobi, Jacobian, Lax, Poisson, Soloviev, The, This, Weinreich
related to Historical elements · 12
Pentagram map → Brianchon's, Clebsch, Desargues's, It, Kasner, Motzkin, Pascal's, Poncelet's, Schwartz, Some, The, Their
related to Arnold–Liouville integrability · 10
Pentagram map → Because, Casimir, Ovsienko, Poisson, Sard's, Schwartz, Tabachnikov, The, This, When
related to Cluster algebras · 9
Pentagram map → Goncharov, Hamiltonians, Kenyon, Lax, Lie, Poisson, The, These, Using
related to Grassmannian polygons · 9
Pentagram map → Consider, GL, Gr, Grassmannian, Hence, Let, The, This, When
related to The spectral curve · 9
Pentagram map → GL, Id, It, Its, Lax, Let, Soloviev, The, Then
related to Generalizations · 8
Pentagram map → Boussinesq, GL, KdV, KP, Not, PDEs, Some, The
related to The Boussinesq equation · 8
Pentagram map → Boussinesq, Given, Here, Moreover, Poisson, The, This, When
related to Exponential shrinking · 6
Pentagram map → Let, One, Richard Schwartz, The, There, This

Important terminology Word statistics

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Important terminology

pentagram displaystyle map doi issn 10 polygons space projective monodromy polygon twisted moduli integrability schwartz maps mathematical plane integrable defined

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Pentagram mapis adiscrete dynamical system acting on polygons in the projective plane0.90text
Pentagram mapis abirational map on the moduli space0.90text
Pentagram mapis aBoussinesq equation0.90text
Pentagram maprelated to Algebro-geometric integrabilityIn0.60section
Pentagram maprelated to Algebro-geometric integrabilitySoloviev0.60section
Pentagram maprelated to Algebro-geometric integrabilityLax0.60section
Pentagram maprelated to Algebro-geometric integrabilityThis0.60section
Pentagram maprelated to Algebro-geometric integrabilityFloquet0.60section
Pentagram maprelated to Algebro-geometric integrabilityBloch0.60section
Pentagram maprelated to Algebro-geometric integrabilityJacobian0.60section
Pentagram maprelated to Algebro-geometric integrabilityAbel0.60section
Pentagram maprelated to Algebro-geometric integrabilityJacobi0.60section

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