Publisher's Synopsis
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
