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Pentagram map: Works, Works cited & Complete integrability

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…

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Pentagram map topic overview

The analysis highlights Works, Works cited and Complete integrability as prominent areas in the source structure around Pentagram map.

Related topics
186
Source areas
12
Connected nodes
198
Extracted relationships
353
Concept neighborhoods
55
Bridge connections
198

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 45 topics
Works cited · 29 topics
Complete integrability · 23 topics
Definitions and first properties · 19 topics
Invariant structures · 14 topics
Collapsing of convex polygons · 11 topics
Connections to other topics · 10 topics
Generalizations · 10 topics
Coordinates for the moduli space · 9 topics
Introduction · 7 topics
Formulas on the moduli space · 5 topics
Periodic orbits on the moduli space · 4 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

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

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Pentagram map connects Entity context

The extracted context around Pentagram map shows recurring relationship patterns in the source. For example, 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 Another extracted example is Pentagram map → Abel, Abelian, Bloch, Floquet, In, Jacobi, Jacobian, Lax, Poisson, Soloviev, The, This, Weinreich. Use these groups to spot repeated connection types before inspecting the individual relationships.

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

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

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

Pentagram map relationships Subject–Predicate–Object triples

TTTA extracted 353 structured relationships around Pentagram map. Examples in this analysis include Pentagram map → is a → discrete dynamical system acting on polygons in the projective plane and Pentagram map → is a → birational map on the moduli space. The table shows each extracted connection, where it came from and its confidence.

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

Related concept clusters Concept neighborhoods

The concept neighborhoods around Pentagram map bring nearby vocabulary together. In this analysis, examples include Pentagram, Schwartz and Polygons. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Pentagram map
    • Pentagram
    • Schwartz
    • Polygons
    • Maps
    • Space
    • Displaystyle
    • Richard
    • Integrability
    • Moduli
    • Also
    • Defined
    • Invariant
  • pentagram map
    • Pentagram
    • Schwartz
    • Polygons
    • Maps
    • Displaystyle
    • Space
    • Moduli
    • Richard
    • Integrability
    • Point
    • Defined
    • Also
  • polygons
    • Closed
    • Space
    • Twisted
    • Projective
    • Plane
    • Moduli
    • Integrability
    • Displaystyle
    • One
    • Defined
    • Mathbb
    • Schwartz
  • projective plane
    • Projective
    • Vertices
    • Polygon
    • Mathbb
    • Polygons
    • Twisted
    • Closed
    • Defined
    • Displaystyle
    • Action
    • Monodromy
    • Also
  • moduli space
    • Space
    • Twisted
    • Displaystyle
    • Action
    • Invariants
    • Polygons
    • Pentagram
    • Mathbb
    • Defined
    • Projective
    • Called
    • Invariant
  • complete integrability
    • Closed
    • Maps
    • Pentagram
    • Twisted
    • Polygons
    • Map
    • Called
    • Moduli
    • Schwartz
    • Polygon
    • Space
    • Arxiv
  • convex polygons
    • Closed
    • Space
    • Twisted
    • Projective
    • Plane
    • Moduli
    • Integrability
    • Displaystyle
    • One
    • Defined
    • Mathbb
    • Schwartz
  • non-convex polygons
    • Closed
    • Space
    • Twisted
    • Projective
    • Plane
    • Moduli
    • Integrability
    • Displaystyle
    • One
    • Defined
    • Mathbb
    • Schwartz

Connections between topic areas Semantic bridges

For Pentagram map, one of the stronger structural bridges in this analysis connects Pentagram map with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Pentagram map — Overview · splits 153 ⟂ 46
Pentagram map — Works cited · splits 169 ⟂ 30
Pentagram map — Complete integrability · splits 175 ⟂ 24
Pentagram map — Definitions and first properties · splits 179 ⟂ 20
Pentagram map — Invariant structures · splits 184 ⟂ 15
Pentagram map — Collapsing of convex polygons · splits 187 ⟂ 12
Pentagram map — Connections to other topics · splits 188 ⟂ 11
Pentagram map — Generalizations · splits 188 ⟂ 11
Pentagram map — Coordinates for the moduli space · splits 189 ⟂ 10
Pentagram map — Introduction · splits 191 ⟂ 8
Pentagram map — Formulas on the moduli space · splits 193 ⟂ 6
Pentagram map — Periodic orbits on the moduli space · splits 194 ⟂ 5

Map overview Semantic statistics

Pentagram map

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

Source & methodology

TTTA analyzes the structure around Pentagram map to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Works, Works cited & Complete integrability, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Pentagram map · EN edition · Analysis: TopicsToTalkAbout

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