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 edges, meanders are introduced from the graphtheoretical perspective. Supplementing the rigorous results, mathematical methods, constructions, and examples of meanders with a large number of insightful figures, issues such as connectivity and the number of connected components of meanders are studied in detail with the aid of collapse and multiple collapse, forks, and chambers. Moreover, the author introduces a large class of Morse meanders by utilizing the right and left one-shift maps, and presents connections to Sturm global attractors, seaweed and Frobenius Lie algebras, and the classical Yang-Baxter equation.

Contents

Seaweed Meanders

Meanders

Morse Meanders and Sturm Global Attractors

Right and Left One-Shifts

Connection Graphs of Type I, II, III and IV

Meanders and the Temperley-Lieb Algebra

Representations of Seaweed Lie Algebras

CYBE and Seaweed Meanders