Meanders : Sturm global attractors, seaweed Lie algebras and classical Yang-Baxter equation

This unique book’s subject is meanders (connected, oriented, non-self-intersecting planar curves intersecting the horizontal line transversely) in the context of dynamical systems. By interpreting the transverse intersection points as vertices and the arches arising from these curves as directed edg...

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Bibliographic Details
Main Author Karnauhova, Anna
Format eBook Book
LanguageEnglish
Published Berlin De Gruyter 2017
Walter de Gruyter GmbH
Edition1
Subjects
Attractors (Mathematics)
Attraktor
Curves, Algebraic
Dynamisches System
Lie algebras
Lie-Algebra
MATHEMATICS / Geometry / General
Morse-Theorie
Yang-Baxter equation
Yang-Baxter-Gleichung
Online AccessGet full text
ISBN9783110531473
311053147X
DOI10.1515/9783110533026

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Table of Contents:
  • 8.1 The Origin of Yang-Baxter Equation -- 8.2 YBE and the Braid Relation -- 8.3 Classical Yang-Baxter Equation (CYBE) -- 8.3.1 Frobenius Lie Algebras and Constant Solutions of CYBE -- Summary in German (Zusammenfassung) -- Bibliography
  • Intro -- Contents -- Preface -- 1. Seaweed Meanders -- 1.1 Seaweed Meanders -- 1.1.1 Collapse Procedure for Seaweed Meanders -- 1.1.2 Collapse: Results on Connectivity -- 1.2 Proof of the Obstruction-Theorem -- 1.2.1 Obstruction-Theorem for Seaweed Meanders: Four Upper Blocks -- 1.2.2 Obstruction-Theorem for Seaweed Meanders with at Least Four Upper Blocks -- 2. Meanders -- 2.1 Collapse of (Closed) Meanders -- 2.2 Results and Examples for Connected Meanders -- 3. Morse Meanders and Sturm Global Attractors -- 3.1 Sturm Global Attractors -- 3.1.1 CW Complexes: Sturm Global Attractors -- 3.2 Morse Meanders -- 3.2.1 Definition of Morse Meanders -- 3.2.2 Raising the Morse Indices -- 4. Right and Left One-Shifts -- 4.1 Morse Meanders of Type I -- 4.2 Morse Meanders of Type II -- 4.3 Morse Meanders of Type III and IV -- 4.4 Sets of Morse Meanders of Type I, II, III, and IV are Disjoint and Consist of Pitchforkable Elements -- 4.5 Detecting Morse Meanders - Discussion -- 5. Connection Graphs of Type I, II, III and IV -- 5.1 Suspensions of Connection Graphs -- 5.2 Construction of Connection Graphs of Type I, II, III and IV -- 5.2.1 Connection Graphs of Type I -- 5.2.2 Isomorphism Class of Type I Connection Graphs -- 5.2.3 Connection Graphs of Type II -- 5.2.4 Isomorphism Class of Type II Connection Graphs -- 5.2.5 Connection Graphs of Type III and IV -- 5.3 Connection Graphs of Different Types Are Non-Isomorphic -- 6. Meanders and the Temperley-Lieb Algebra -- 6.1 From Open Meanders to Closed Meanders -- 6.2 From Blocks to Strand Diagrams -- 6.3 Temperley-Lieb Algebra -- 6.4 Left and Right One-Shifts in Terms of Temperley-Lieb Algebra -- 7. Representations of Seaweed Lie Algebras -- 7.1 Index of a Lie Algebra -- 7.2 Seaweed Lie Algebras -- 7.3 Graph Representations of Seaweed Lie Algebras -- 8. CYBE and Seaweed Meanders
  • 1. Seaweed Meanders --
  • 6. Meanders and the Temperley–Lieb Algebra --
  • Contents --
  • 7. Seaweed Lie Algebras and Seaweed Meanders --
  • Preface --
  • 5. Connection Graphs of Type I, II, III and IV --
  • 3. Morse Meanders and Sturm Global Attractors --
  • 8. Classical Yang–Baxter Equation and Seaweed Meanders --
  • 2. Meanders --
  • Frontmatter --
  • 4. Right and Left One-Shifts --
  • Bibliography
  • Summary in German (Zusammenfassung) --